TY  - CONF
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2016
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2665
AB  - We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
PB  - Amer Inst Physics, Melville
C3  - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce
T1  - Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units
VL  - 1738
DO  - 10.1063/1.4951987
ER  - 

@conference{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2016",
abstract = "We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.",
publisher = "Amer Inst Physics, Melville",
journal = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce",
title = "Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units",
volume = "1738",
doi = "10.1063/1.4951987"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2016). Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units. in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce
Amer Inst Physics, Melville., 1738.
https://doi.org/10.1063/1.4951987

Franović I, Todorović K, Vasović N, Burić N. Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units. in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce. 2016;1738.
doi:10.1063/1.4951987 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units" in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce, 1738 (2016),
https://doi.org/10.1063/1.4951987 . .

TY  - JOUR
AU  - Grozdanović, Ines
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
AU  - Trisović, Nataša
PY  - 2015
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2469
AB  - Numerical study of variations in coherence of spike trains produced by two stochastically perturbed FitzHugh-Nagumo excitable systems with internal and coupling time-delays is performed. Both, the internal time-delay and the interaction time-delay in some domains of values can substantially increase the coherence but the interplay of the two delays can also lead to quite incoherent spike trains. Numerically observed dependence of the coherence on the delays is qualitatively explained by considering the bifurcations in the system caused by the variations of the values of the internal and the interaction time-lags.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - International Journal of Non-Linear Mechanics
T1  - Interplay between internal delays and coherent oscillations in delayed coupled noisy excitable systems
VL  - 73
SP  - 121
EP  - 127
DO  - 10.1016/j.ijnonlinmec.2014.11.010
ER  - 

@article{
author = "Grozdanović, Ines and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola and Trisović, Nataša",
year = "2015",
abstract = "Numerical study of variations in coherence of spike trains produced by two stochastically perturbed FitzHugh-Nagumo excitable systems with internal and coupling time-delays is performed. Both, the internal time-delay and the interaction time-delay in some domains of values can substantially increase the coherence but the interplay of the two delays can also lead to quite incoherent spike trains. Numerically observed dependence of the coherence on the delays is qualitatively explained by considering the bifurcations in the system caused by the variations of the values of the internal and the interaction time-lags.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "International Journal of Non-Linear Mechanics",
title = "Interplay between internal delays and coherent oscillations in delayed coupled noisy excitable systems",
volume = "73",
pages = "121-127",
doi = "10.1016/j.ijnonlinmec.2014.11.010"
}

Grozdanović, I., Todorović, K., Vasović, N., Burić, N.,& Trisović, N.. (2015). Interplay between internal delays and coherent oscillations in delayed coupled noisy excitable systems. in International Journal of Non-Linear Mechanics
Pergamon-Elsevier Science Ltd, Oxford., 73, 121-127.
https://doi.org/10.1016/j.ijnonlinmec.2014.11.010

Grozdanović I, Todorović K, Vasović N, Burić N, Trisović N. Interplay between internal delays and coherent oscillations in delayed coupled noisy excitable systems. in International Journal of Non-Linear Mechanics. 2015;73:121-127.
doi:10.1016/j.ijnonlinmec.2014.11.010 .

Grozdanović, Ines, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, Trisović, Nataša, "Interplay between internal delays and coherent oscillations in delayed coupled noisy excitable systems" in International Journal of Non-Linear Mechanics, 73 (2015):121-127,
https://doi.org/10.1016/j.ijnonlinmec.2014.11.010 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Perc, Matjaz
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2015
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2311
AB  - We consider the coaction of two distinct noise sources on the activation process of a single excitable unit and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving two coupled units. We analyze the effects of the two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear or nonlinear form of interactions. Universal properties of the activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Activation process in excitable systems with multiple noise sources: One and two interacting units
VL  - 92
IS  - 6
DO  - 10.1103/PhysRevE.92.062911
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Perc, Matjaz and Vasović, Nebojša and Burić, Nikola",
year = "2015",
abstract = "We consider the coaction of two distinct noise sources on the activation process of a single excitable unit and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving two coupled units. We analyze the effects of the two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear or nonlinear form of interactions. Universal properties of the activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Activation process in excitable systems with multiple noise sources: One and two interacting units",
volume = "92",
number = "6",
doi = "10.1103/PhysRevE.92.062911"
}

Franović, I., Todorović, K., Perc, M., Vasović, N.,& Burić, N.. (2015). Activation process in excitable systems with multiple noise sources: One and two interacting units. in Physical Review E
Amer Physical Soc, College Pk., 92(6).
https://doi.org/10.1103/PhysRevE.92.062911

Franović I, Todorović K, Perc M, Vasović N, Burić N. Activation process in excitable systems with multiple noise sources: One and two interacting units. in Physical Review E. 2015;92(6).
doi:10.1103/PhysRevE.92.062911 .

Franović, Igor, Todorović, Kristina, Perc, Matjaz, Vasović, Nebojša, Burić, Nikola, "Activation process in excitable systems with multiple noise sources: One and two interacting units" in Physical Review E, 92, no. 6 (2015),
https://doi.org/10.1103/PhysRevE.92.062911 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Perc, Matjaz
AU  - Todorović, Kristina
AU  - Kostić, Srđan
AU  - Burić, Nikola
PY  - 2015
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2309
AB  - We study the activation process in large assemblies of type II excitable units whose dynamics is influenced by two independent noise terms. The mean-field approach is applied to explicitly demonstrate that the assembly of excitable units can itself exhibit macroscopic excitable behavior. In order to facilitate the comparison between the excitable dynamics of a single unit and an assembly, we introduce three distinct formulations of the assembly activation event. Each formulation treats different aspects of the relevant phenomena, including the thresholdlike behavior and the role of coherence of individual spikes. Statistical properties of the assembly activation process, such as the mean time-to-first pulse and the associated coefficient of variation, are found to be qualitatively analogous for all three formulations, as well as to resemble the results for a single unit. These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations. Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics. We also briefly report on a system-size antiresonant effect displayed by the mean time-to-first pulse.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Activation process in excitable systems with multiple noise sources: Large number of units
VL  - 92
IS  - 6
DO  - 10.1103/PhysRevE.92.062912
ER  - 

@article{
author = "Franović, Igor and Perc, Matjaz and Todorović, Kristina and Kostić, Srđan and Burić, Nikola",
year = "2015",
abstract = "We study the activation process in large assemblies of type II excitable units whose dynamics is influenced by two independent noise terms. The mean-field approach is applied to explicitly demonstrate that the assembly of excitable units can itself exhibit macroscopic excitable behavior. In order to facilitate the comparison between the excitable dynamics of a single unit and an assembly, we introduce three distinct formulations of the assembly activation event. Each formulation treats different aspects of the relevant phenomena, including the thresholdlike behavior and the role of coherence of individual spikes. Statistical properties of the assembly activation process, such as the mean time-to-first pulse and the associated coefficient of variation, are found to be qualitatively analogous for all three formulations, as well as to resemble the results for a single unit. These analogies are shown to derive from the fact that global variables undergo a stochastic bifurcation from the stochastically stable fixed point to continuous oscillations. Local activation processes are analyzed in the light of the competition between the noise-led and the relaxation-driven dynamics. We also briefly report on a system-size antiresonant effect displayed by the mean time-to-first pulse.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Activation process in excitable systems with multiple noise sources: Large number of units",
volume = "92",
number = "6",
doi = "10.1103/PhysRevE.92.062912"
}

Franović, I., Perc, M., Todorović, K., Kostić, S.,& Burić, N.. (2015). Activation process in excitable systems with multiple noise sources: Large number of units. in Physical Review E
Amer Physical Soc, College Pk., 92(6).
https://doi.org/10.1103/PhysRevE.92.062912

Franović I, Perc M, Todorović K, Kostić S, Burić N. Activation process in excitable systems with multiple noise sources: Large number of units. in Physical Review E. 2015;92(6).
doi:10.1103/PhysRevE.92.062912 .

Franović, Igor, Perc, Matjaz, Todorović, Kristina, Kostić, Srđan, Burić, Nikola, "Activation process in excitable systems with multiple noise sources: Large number of units" in Physical Review E, 92, no. 6 (2015),
https://doi.org/10.1103/PhysRevE.92.062912 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2014
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2181
AB  - We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units
VL  - 89
IS  - 2
DO  - 10.1103/PhysRevE.89.022926
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2014",
abstract = "We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units",
volume = "89",
number = "2",
doi = "10.1103/PhysRevE.89.022926"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2014). Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units. in Physical Review E
Amer Physical Soc, College Pk., 89(2).
https://doi.org/10.1103/PhysRevE.89.022926

Franović I, Todorović K, Vasović N, Burić N. Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units. in Physical Review E. 2014;89(2).
doi:10.1103/PhysRevE.89.022926 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units" in Physical Review E, 89, no. 2 (2014),
https://doi.org/10.1103/PhysRevE.89.022926 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2014
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2166
AB  - We study the onset and the adjustment of different oscillatory modes in a system of excitable units subjected to two forms of noise and delays cast as external or internal according to whether they are associated with inter- or intra-unit activity. Conditions for stability of a single unit are derived in case of the linearized perturbed system, whereas the interplay of noise and internal delay in shaping the oscillatory motion is analyzed by the method of statistical linearization. It is demonstrated that the internal delay, as well as its coaction with external noise, drive the unit away from the bifurcation controlled by the excitability parameter. For the pair of interacting units, it is shown that the external/internal character of noise primarily influences frequency synchronization and the competition between the noise-induced and delay-driven oscillatory modes, while coherence of firing and phase synchronization substantially depend on internal delay. Some of the important effects include: (i) loss of frequency synchronization under external noise; (ii) existence of characteristic regimes of entrainment, where under variation of coupling delay, the optimized unit (noise intensity fixed at resonant value) may be controlled by the adjustable unit (variable noise) and vice versa, or both units may become adjusted to coupling delay; (iii) phase synchronization achieved both for noise-induced and delay-driven modes.
PB  - Elsevier Science BV, Amsterdam
T2  - Communications in Nonlinear Science and Numerical Simulation
T1  - Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays
VL  - 19
IS  - 9
SP  - 3202
EP  - 3219
DO  - 10.1016/j.cnsns.2014.02.022
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2014",
abstract = "We study the onset and the adjustment of different oscillatory modes in a system of excitable units subjected to two forms of noise and delays cast as external or internal according to whether they are associated with inter- or intra-unit activity. Conditions for stability of a single unit are derived in case of the linearized perturbed system, whereas the interplay of noise and internal delay in shaping the oscillatory motion is analyzed by the method of statistical linearization. It is demonstrated that the internal delay, as well as its coaction with external noise, drive the unit away from the bifurcation controlled by the excitability parameter. For the pair of interacting units, it is shown that the external/internal character of noise primarily influences frequency synchronization and the competition between the noise-induced and delay-driven oscillatory modes, while coherence of firing and phase synchronization substantially depend on internal delay. Some of the important effects include: (i) loss of frequency synchronization under external noise; (ii) existence of characteristic regimes of entrainment, where under variation of coupling delay, the optimized unit (noise intensity fixed at resonant value) may be controlled by the adjustable unit (variable noise) and vice versa, or both units may become adjusted to coupling delay; (iii) phase synchronization achieved both for noise-induced and delay-driven modes.",
publisher = "Elsevier Science BV, Amsterdam",
journal = "Communications in Nonlinear Science and Numerical Simulation",
title = "Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays",
volume = "19",
number = "9",
pages = "3202-3219",
doi = "10.1016/j.cnsns.2014.02.022"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2014). Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays. in Communications in Nonlinear Science and Numerical Simulation
Elsevier Science BV, Amsterdam., 19(9), 3202-3219.
https://doi.org/10.1016/j.cnsns.2014.02.022

Franović I, Todorović K, Vasović N, Burić N. Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays. in Communications in Nonlinear Science and Numerical Simulation. 2014;19(9):3202-3219.
doi:10.1016/j.cnsns.2014.02.022 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays" in Communications in Nonlinear Science and Numerical Simulation, 19, no. 9 (2014):3202-3219,
https://doi.org/10.1016/j.cnsns.2014.02.022 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2013
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1948
AB  - The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings. DOI: 10.1103/PhysRevE.87.012922
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Mean-field approximation of two coupled populations of excitable units
VL  - 87
IS  - 1
DO  - 10.1103/PhysRevE.87.012922
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2013",
abstract = "The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings. DOI: 10.1103/PhysRevE.87.012922",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Mean-field approximation of two coupled populations of excitable units",
volume = "87",
number = "1",
doi = "10.1103/PhysRevE.87.012922"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2013). Mean-field approximation of two coupled populations of excitable units. in Physical Review E
Amer Physical Soc, College Pk., 87(1).
https://doi.org/10.1103/PhysRevE.87.012922

Franović I, Todorović K, Vasović N, Burić N. Mean-field approximation of two coupled populations of excitable units. in Physical Review E. 2013;87(1).
doi:10.1103/PhysRevE.87.012922 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Mean-field approximation of two coupled populations of excitable units" in Physical Review E, 87, no. 1 (2013),
https://doi.org/10.1103/PhysRevE.87.012922 . .

TY  - JOUR
AU  - Vasović, Nebojša
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Grozdanović, Ines
PY  - 2012
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1725
AB  - The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.
PB  - Iop Publishing Ltd, Bristol
T2  - Chinese Physics B
T1  - Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses
VL  - 21
IS  - 1
DO  - 10.1088/1674-1056/21/1/010203
ER  - 

@article{
author = "Vasović, Nebojša and Burić, Nikola and Todorović, Kristina and Grozdanović, Ines",
year = "2012",
abstract = "The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.",
publisher = "Iop Publishing Ltd, Bristol",
journal = "Chinese Physics B",
title = "Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses",
volume = "21",
number = "1",
doi = "10.1088/1674-1056/21/1/010203"
}

Vasović, N., Burić, N., Todorović, K.,& Grozdanović, I.. (2012). Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses. in Chinese Physics B
Iop Publishing Ltd, Bristol., 21(1).
https://doi.org/10.1088/1674-1056/21/1/010203

Vasović N, Burić N, Todorović K, Grozdanović I. Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses. in Chinese Physics B. 2012;21(1).
doi:10.1088/1674-1056/21/1/010203 .

Vasović, Nebojša, Burić, Nikola, Todorović, Kristina, Grozdanović, Ines, "Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses" in Chinese Physics B, 21, no. 1 (2012),
https://doi.org/10.1088/1674-1056/21/1/010203 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2012
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1695
AB  - The spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise, and the excitable character of a single neuron. The dependence of the cluster properties on the time lag, noise intensity, and the synaptic strength is investigated.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review Letters
T1  - Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays
VL  - 108
IS  - 9
DO  - 10.1103/PhysRevLett.108.094101
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2012",
abstract = "The spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise, and the excitable character of a single neuron. The dependence of the cluster properties on the time lag, noise intensity, and the synaptic strength is investigated.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review Letters",
title = "Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays",
volume = "108",
number = "9",
doi = "10.1103/PhysRevLett.108.094101"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2012). Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays. in Physical Review Letters
Amer Physical Soc, College Pk., 108(9).
https://doi.org/10.1103/PhysRevLett.108.094101

Franović I, Todorović K, Vasović N, Burić N. Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays. in Physical Review Letters. 2012;108(9).
doi:10.1103/PhysRevLett.108.094101 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Spontaneous Formation of Synchronization Clusters in Homogenous Neuronal Ensembles Induced by Noise and Interaction Delays" in Physical Review Letters, 108, no. 9 (2012),
https://doi.org/10.1103/PhysRevLett.108.094101 . .

TY  - CONF
AU  - Vasović, Nebojša
AU  - Burić, Nikola
AU  - Grozdanović, Ines
AU  - Todorović, Kristina
AU  - Samčović, Andreja
PY  - 2012
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1666
AB  - Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag tau >= 1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal-to-noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags tau  lt  1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.
PB  - IEEE, New York
C3  - 11th Symposium on Neural Network Applications in Electrical Engineering,NEUREL 2012 - Proceedings
T1  - Coherent Oscillations in Minimal Neural Network of Excitable Systems Induced by Noise and Influenced by Time Delay
DO  - 10.1109/NEUREL.2012.6419957
ER  - 

@conference{
author = "Vasović, Nebojša and Burić, Nikola and Grozdanović, Ines and Todorović, Kristina and Samčović, Andreja",
year = "2012",
abstract = "Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag tau >= 1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal-to-noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags tau  lt  1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.",
publisher = "IEEE, New York",
journal = "11th Symposium on Neural Network Applications in Electrical Engineering,NEUREL 2012 - Proceedings",
title = "Coherent Oscillations in Minimal Neural Network of Excitable Systems Induced by Noise and Influenced by Time Delay",
doi = "10.1109/NEUREL.2012.6419957"
}

Vasović, N., Burić, N., Grozdanović, I., Todorović, K.,& Samčović, A.. (2012). Coherent Oscillations in Minimal Neural Network of Excitable Systems Induced by Noise and Influenced by Time Delay. in 11th Symposium on Neural Network Applications in Electrical Engineering,NEUREL 2012 - Proceedings
IEEE, New York..
https://doi.org/10.1109/NEUREL.2012.6419957

Vasović N, Burić N, Grozdanović I, Todorović K, Samčović A. Coherent Oscillations in Minimal Neural Network of Excitable Systems Induced by Noise and Influenced by Time Delay. in 11th Symposium on Neural Network Applications in Electrical Engineering,NEUREL 2012 - Proceedings. 2012;.
doi:10.1109/NEUREL.2012.6419957 .

Vasović, Nebojša, Burić, Nikola, Grozdanović, Ines, Todorović, Kristina, Samčović, Andreja, "Coherent Oscillations in Minimal Neural Network of Excitable Systems Induced by Noise and Influenced by Time Delay" in 11th Symposium on Neural Network Applications in Electrical Engineering,NEUREL 2012 - Proceedings (2012),
https://doi.org/10.1109/NEUREL.2012.6419957 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2012
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1647
AB  - Properties of spontaneously formed clusters of synchronous dynamics in a structureless network of noisy excitable neurons connected via delayed diffusive couplings are studied in detail. Several tools have been applied to characterize the synchronization clusters and to study their dependence on the neuronal and the synaptic parameters. Qualitative explanation of the cluster formation is discussed. The interplay between the noise, the interaction time-delay and the excitable character of the neuronal dynamics is shown to be necessary and sufficient for the occurrence of the synchronization clusters. We have found the two-cluster partitions where neurons are firmly bound to their subsets, as well as the three-cluster ones, which are dynamical by nature. The former turn out to be stable under small disparity of the intrinsic neuronal parameters and the heterogeneity in the synaptic connectivity patterns.
PB  - Amer Inst Physics, Melville
T2  - Chaos
T1  - Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles
VL  - 22
IS  - 3
DO  - 10.1063/1.4753919
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2012",
abstract = "Properties of spontaneously formed clusters of synchronous dynamics in a structureless network of noisy excitable neurons connected via delayed diffusive couplings are studied in detail. Several tools have been applied to characterize the synchronization clusters and to study their dependence on the neuronal and the synaptic parameters. Qualitative explanation of the cluster formation is discussed. The interplay between the noise, the interaction time-delay and the excitable character of the neuronal dynamics is shown to be necessary and sufficient for the occurrence of the synchronization clusters. We have found the two-cluster partitions where neurons are firmly bound to their subsets, as well as the three-cluster ones, which are dynamical by nature. The former turn out to be stable under small disparity of the intrinsic neuronal parameters and the heterogeneity in the synaptic connectivity patterns.",
publisher = "Amer Inst Physics, Melville",
journal = "Chaos",
title = "Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles",
volume = "22",
number = "3",
doi = "10.1063/1.4753919"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2012). Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles. in Chaos
Amer Inst Physics, Melville., 22(3).
https://doi.org/10.1063/1.4753919

Franović I, Todorović K, Vasović N, Burić N. Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles. in Chaos. 2012;22(3).
doi:10.1063/1.4753919 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles" in Chaos, 22, no. 3 (2012),
https://doi.org/10.1063/1.4753919 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Grozdanović, Ines
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2011
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1505
AB  - Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag tau >= 1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal to noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags tau  lt  1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.
PB  - Springer, New York
T2  - Journal of Statistical Physics
T1  - Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems
VL  - 145
IS  - 1
SP  - 175
EP  - 186
DO  - 10.1007/s10955-011-0316-6
ER  - 

@article{
author = "Burić, Nikola and Grozdanović, Ines and Todorović, Kristina and Vasović, Nebojša",
year = "2011",
abstract = "Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag tau >= 1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal to noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags tau  lt  1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.",
publisher = "Springer, New York",
journal = "Journal of Statistical Physics",
title = "Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems",
volume = "145",
number = "1",
pages = "175-186",
doi = "10.1007/s10955-011-0316-6"
}

Burić, N., Grozdanović, I., Todorović, K.,& Vasović, N.. (2011). Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems. in Journal of Statistical Physics
Springer, New York., 145(1), 175-186.
https://doi.org/10.1007/s10955-011-0316-6

Burić N, Grozdanović I, Todorović K, Vasović N. Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems. in Journal of Statistical Physics. 2011;145(1):175-186.
doi:10.1007/s10955-011-0316-6 .

Burić, Nikola, Grozdanović, Ines, Todorović, Kristina, Vasović, Nebojša, "Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems" in Journal of Statistical Physics, 145, no. 1 (2011):175-186,
https://doi.org/10.1007/s10955-011-0316-6 . .

TY  - JOUR
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Burić, Nikola
PY  - 2011
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1457
AB  - An approximate mean field model of an ensemble of delayed coupled stochastic Hindmarsh-Rose bursting neurons is constructed and analyzed. Bifurcation analysis of the approximate system is performed using numerical continuation. It is demonstrated that the stability domains in the parameter space of the large exact systems are correctly estimated using the much simpler approximate model.
PB  - Amer Inst Physics, Melville
T2  - Chaos
T1  - Stability, bifurcations, and dynamics of global variables of a system of bursting neurons
VL  - 21
IS  - 3
DO  - 10.1063/1.3619293
ER  - 

@article{
author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola",
year = "2011",
abstract = "An approximate mean field model of an ensemble of delayed coupled stochastic Hindmarsh-Rose bursting neurons is constructed and analyzed. Bifurcation analysis of the approximate system is performed using numerical continuation. It is demonstrated that the stability domains in the parameter space of the large exact systems are correctly estimated using the much simpler approximate model.",
publisher = "Amer Inst Physics, Melville",
journal = "Chaos",
title = "Stability, bifurcations, and dynamics of global variables of a system of bursting neurons",
volume = "21",
number = "3",
doi = "10.1063/1.3619293"
}

Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2011). Stability, bifurcations, and dynamics of global variables of a system of bursting neurons. in Chaos
Amer Inst Physics, Melville., 21(3).
https://doi.org/10.1063/1.3619293

Franović I, Todorović K, Vasović N, Burić N. Stability, bifurcations, and dynamics of global variables of a system of bursting neurons. in Chaos. 2011;21(3).
doi:10.1063/1.3619293 .

Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Stability, bifurcations, and dynamics of global variables of a system of bursting neurons" in Chaos, 21, no. 3 (2011),
https://doi.org/10.1063/1.3619293 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Ranković, Dragana
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2010
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1344
AB  - Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by N >> 1 stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.
PB  - Elsevier Science BV, Amsterdam
T2  - Physica A-Statistical Mechanics and Its Applications
T1  - Mean field approximation for noisy delay coupled excitable neurons
VL  - 389
IS  - 19
SP  - 3956
EP  - 3964
DO  - 10.1016/j.physa.2010.05.048
ER  - 

@article{
author = "Burić, Nikola and Ranković, Dragana and Todorović, Kristina and Vasović, Nebojša",
year = "2010",
abstract = "Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by N >> 1 stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.",
publisher = "Elsevier Science BV, Amsterdam",
journal = "Physica A-Statistical Mechanics and Its Applications",
title = "Mean field approximation for noisy delay coupled excitable neurons",
volume = "389",
number = "19",
pages = "3956-3964",
doi = "10.1016/j.physa.2010.05.048"
}

Burić, N., Ranković, D., Todorović, K.,& Vasović, N.. (2010). Mean field approximation for noisy delay coupled excitable neurons. in Physica A-Statistical Mechanics and Its Applications
Elsevier Science BV, Amsterdam., 389(19), 3956-3964.
https://doi.org/10.1016/j.physa.2010.05.048

Burić N, Ranković D, Todorović K, Vasović N. Mean field approximation for noisy delay coupled excitable neurons. in Physica A-Statistical Mechanics and Its Applications. 2010;389(19):3956-3964.
doi:10.1016/j.physa.2010.05.048 .

Burić, Nikola, Ranković, Dragana, Todorović, Kristina, Vasović, Nebojša, "Mean field approximation for noisy delay coupled excitable neurons" in Physica A-Statistical Mechanics and Its Applications, 389, no. 19 (2010):3956-3964,
https://doi.org/10.1016/j.physa.2010.05.048 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2010
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1329
AB  - Influence of the interaction time delay on the noise-induced system size resonance in a system of all-to-all electrically coupled FitzHugh-Nagumo excitable neurons is studied. It is observed that small time lags decrease and that large time lags increase the coherence of spiking. Bifurcations of the system's stationary state are used to explain the observed nonmonotonic dependence of coherence on the time lag.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Influence of interaction delays on noise-induced coherence in excitable systems
VL  - 82
IS  - 3
DO  - 10.1103/PhysRevE.82.037201
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2010",
abstract = "Influence of the interaction time delay on the noise-induced system size resonance in a system of all-to-all electrically coupled FitzHugh-Nagumo excitable neurons is studied. It is observed that small time lags decrease and that large time lags increase the coherence of spiking. Bifurcations of the system's stationary state are used to explain the observed nonmonotonic dependence of coherence on the time lag.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Influence of interaction delays on noise-induced coherence in excitable systems",
volume = "82",
number = "3",
doi = "10.1103/PhysRevE.82.037201"
}

Burić, N., Todorović, K.,& Vasović, N.. (2010). Influence of interaction delays on noise-induced coherence in excitable systems. in Physical Review E
Amer Physical Soc, College Pk., 82(3).
https://doi.org/10.1103/PhysRevE.82.037201

Burić N, Todorović K, Vasović N. Influence of interaction delays on noise-induced coherence in excitable systems. in Physical Review E. 2010;82(3).
doi:10.1103/PhysRevE.82.037201 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Influence of interaction delays on noise-induced coherence in excitable systems" in Physical Review E, 82, no. 3 (2010),
https://doi.org/10.1103/PhysRevE.82.037201 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2009
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1237
AB  - Results of an extensive numerical Study of the influence of additive white noise oil the dynamics of a pair of delayed Coupled FitzHugh-Nagumo neurons Lire presented. An intuitively clear simple method is utilized to predict the critical intensities of the noise. In general, the qualitative properties of file noiseless dynamics are stable under the influence of the noise of a reasonable magnitude. However, there Lire regions Of file Coupling and time-lag parameters where the noise of a physically acceptable magnitude does cause qualitative changes of the dynamics. These regions Lire Studied in detail.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - Chaos Solitons & Fractals
T1  - Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling
VL  - 40
IS  - 5
SP  - 2405
EP  - 2413
DO  - 10.1016/j.chaos.2007.10.036
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2009",
abstract = "Results of an extensive numerical Study of the influence of additive white noise oil the dynamics of a pair of delayed Coupled FitzHugh-Nagumo neurons Lire presented. An intuitively clear simple method is utilized to predict the critical intensities of the noise. In general, the qualitative properties of file noiseless dynamics are stable under the influence of the noise of a reasonable magnitude. However, there Lire regions Of file Coupling and time-lag parameters where the noise of a physically acceptable magnitude does cause qualitative changes of the dynamics. These regions Lire Studied in detail.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "Chaos Solitons & Fractals",
title = "Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling",
volume = "40",
number = "5",
pages = "2405-2413",
doi = "10.1016/j.chaos.2007.10.036"
}

Burić, N., Todorović, K.,& Vasović, N.. (2009). Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling. in Chaos Solitons & Fractals
Pergamon-Elsevier Science Ltd, Oxford., 40(5), 2405-2413.
https://doi.org/10.1016/j.chaos.2007.10.036

Burić N, Todorović K, Vasović N. Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling. in Chaos Solitons & Fractals. 2009;40(5):2405-2413.
doi:10.1016/j.chaos.2007.10.036 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Dynamics of noisy FitzHugh-Nagumo neurons with delayed coupling" in Chaos Solitons & Fractals, 40, no. 5 (2009):2405-2413,
https://doi.org/10.1016/j.chaos.2007.10.036 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2009
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1216
AB  - Exact synchronization of a pair of stochastically perturbed Hindmarsh-Rose bursting neurons with delayed electrical coupling is studied. Possibility of stochastically stable exact synchronization with sufficiently strong coupling is proved for arbitrary time-lags and sufficiently small noise. Various effects of the interplay and influence of noise and time-delay oil the exact synchrony are studied by numerical computations.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - Chaos Solitons & Fractals
T1  - Exact synchronization of noisy bursting neurons with coupling delays
VL  - 40
IS  - 3
SP  - 1127
EP  - 1135
DO  - 10.1016/j.chaos.2007.08.067
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2009",
abstract = "Exact synchronization of a pair of stochastically perturbed Hindmarsh-Rose bursting neurons with delayed electrical coupling is studied. Possibility of stochastically stable exact synchronization with sufficiently strong coupling is proved for arbitrary time-lags and sufficiently small noise. Various effects of the interplay and influence of noise and time-delay oil the exact synchrony are studied by numerical computations.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "Chaos Solitons & Fractals",
title = "Exact synchronization of noisy bursting neurons with coupling delays",
volume = "40",
number = "3",
pages = "1127-1135",
doi = "10.1016/j.chaos.2007.08.067"
}

Burić, N., Todorović, K.,& Vasović, N.. (2009). Exact synchronization of noisy bursting neurons with coupling delays. in Chaos Solitons & Fractals
Pergamon-Elsevier Science Ltd, Oxford., 40(3), 1127-1135.
https://doi.org/10.1016/j.chaos.2007.08.067

Burić N, Todorović K, Vasović N. Exact synchronization of noisy bursting neurons with coupling delays. in Chaos Solitons & Fractals. 2009;40(3):1127-1135.
doi:10.1016/j.chaos.2007.08.067 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Exact synchronization of noisy bursting neurons with coupling delays" in Chaos Solitons & Fractals, 40, no. 3 (2009):1127-1135,
https://doi.org/10.1016/j.chaos.2007.08.067 . .

TY  - CONF
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
AU  - Samcović, Andreja
PY  - 2008
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1044
AB  - Synchronization patterns in chains of N bi-directionally delayed coupled systems with delayed feedback are studied in this paper. Each system is hyper-chaotic when decoupled from the chain. It is shown that chains with odd or even number of cites N display different spatial patterns of stable exact synchronization. When N is odd the only stable pattern of exact synchronization is among all of the units. When N is even, next to the nearest neighbors could become exactly synchronized, with the dynamics of the nearest neighbors related in a more complicated way. Sufficiently strong coupling leads to the nearest neighbor synchronization also for even N. No other patterns have been observed.
PB  - IEEE, New York
C3  - 9th Symposium on Neural Network Applications in Electrical Engineering, NEUREL 2008 Proceedings
T1  - Synchronization Patterns in Neural Chains based on Hyper-Chaotic Cells
SP  - 51
DO  - 10.1109/NEUREL.2008.4685559
ER  - 

@conference{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša and Samcović, Andreja",
year = "2008",
abstract = "Synchronization patterns in chains of N bi-directionally delayed coupled systems with delayed feedback are studied in this paper. Each system is hyper-chaotic when decoupled from the chain. It is shown that chains with odd or even number of cites N display different spatial patterns of stable exact synchronization. When N is odd the only stable pattern of exact synchronization is among all of the units. When N is even, next to the nearest neighbors could become exactly synchronized, with the dynamics of the nearest neighbors related in a more complicated way. Sufficiently strong coupling leads to the nearest neighbor synchronization also for even N. No other patterns have been observed.",
publisher = "IEEE, New York",
journal = "9th Symposium on Neural Network Applications in Electrical Engineering, NEUREL 2008 Proceedings",
title = "Synchronization Patterns in Neural Chains based on Hyper-Chaotic Cells",
pages = "51",
doi = "10.1109/NEUREL.2008.4685559"
}

Burić, N., Todorović, K., Vasović, N.,& Samcović, A.. (2008). Synchronization Patterns in Neural Chains based on Hyper-Chaotic Cells. in 9th Symposium on Neural Network Applications in Electrical Engineering, NEUREL 2008 Proceedings
IEEE, New York., 51.
https://doi.org/10.1109/NEUREL.2008.4685559

Burić N, Todorović K, Vasović N, Samcović A. Synchronization Patterns in Neural Chains based on Hyper-Chaotic Cells. in 9th Symposium on Neural Network Applications in Electrical Engineering, NEUREL 2008 Proceedings. 2008;:51.
doi:10.1109/NEUREL.2008.4685559 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, Samcović, Andreja, "Synchronization Patterns in Neural Chains based on Hyper-Chaotic Cells" in 9th Symposium on Neural Network Applications in Electrical Engineering, NEUREL 2008 Proceedings (2008):51,
https://doi.org/10.1109/NEUREL.2008.4685559 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2008
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1035
AB  - The synchronization of bursting Hindmarsh-Rose neurons coupled by a time-delayed fast threshold modulation synapse was studied. It is shown that there is a domain of the coupling parameter and nonzero time-lag values such that the bursting neurons are exactly synchronized. Furthermore, and contrary to the case of electrical synapses, such synchronous bursting is stochastically stable.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Synchronization of bursting neurons with delayed chemical synapses
VL  - 78
IS  - 3
DO  - 10.1103/PhysRevE.78.036211
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2008",
abstract = "The synchronization of bursting Hindmarsh-Rose neurons coupled by a time-delayed fast threshold modulation synapse was studied. It is shown that there is a domain of the coupling parameter and nonzero time-lag values such that the bursting neurons are exactly synchronized. Furthermore, and contrary to the case of electrical synapses, such synchronous bursting is stochastically stable.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Synchronization of bursting neurons with delayed chemical synapses",
volume = "78",
number = "3",
doi = "10.1103/PhysRevE.78.036211"
}

Burić, N., Todorović, K.,& Vasović, N.. (2008). Synchronization of bursting neurons with delayed chemical synapses. in Physical Review E
Amer Physical Soc, College Pk., 78(3).
https://doi.org/10.1103/PhysRevE.78.036211

Burić N, Todorović K, Vasović N. Synchronization of bursting neurons with delayed chemical synapses. in Physical Review E. 2008;78(3).
doi:10.1103/PhysRevE.78.036211 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Synchronization of bursting neurons with delayed chemical synapses" in Physical Review E, 78, no. 3 (2008),
https://doi.org/10.1103/PhysRevE.78.036211 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2007
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/951
AB  - Synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied, using as an example circular chains of three and four delayed coupled Ikeda oscillators. It is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling, and an analytic estimate of the sufficient coupling is given. The sufficiency condition is compared with numerical computations, and typical effects of noise on the exact and some generalized types of synchronization are illustrated.
PB  - American Physical Soc, College Pk
T2  - Physical Review E
T1  - Synchronization of noisy delayed feedback systems with delayed coupling
VL  - 75
IS  - 2
DO  - 10.1103/PhysRevE.75.026209
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2007",
abstract = "Synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied, using as an example circular chains of three and four delayed coupled Ikeda oscillators. It is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling, and an analytic estimate of the sufficient coupling is given. The sufficiency condition is compared with numerical computations, and typical effects of noise on the exact and some generalized types of synchronization are illustrated.",
publisher = "American Physical Soc, College Pk",
journal = "Physical Review E",
title = "Synchronization of noisy delayed feedback systems with delayed coupling",
volume = "75",
number = "2",
doi = "10.1103/PhysRevE.75.026209"
}

Burić, N., Todorović, K.,& Vasović, N.. (2007). Synchronization of noisy delayed feedback systems with delayed coupling. in Physical Review E
American Physical Soc, College Pk., 75(2).
https://doi.org/10.1103/PhysRevE.75.026209

Burić N, Todorović K, Vasović N. Synchronization of noisy delayed feedback systems with delayed coupling. in Physical Review E. 2007;75(2).
doi:10.1103/PhysRevE.75.026209 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Synchronization of noisy delayed feedback systems with delayed coupling" in Physical Review E, 75, no. 2 (2007),
https://doi.org/10.1103/PhysRevE.75.026209 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2007
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/929
AB  - The influence of white noise on the dynamics of a delayed electrically coupled pair of Hidmarsh-Rose bursting neurons is studied. In particular a simple method to predict the intensity of noise that can destabilize the quiescent state is proposed and compared with numerical computations. Furthermore, it is demonstrated that quite small noise completely destroys the exact synchronization of bursting dynamics, and a qualitative explanation of this effect is discussed.
PB  - Amer Physical Soc, College Pk
T2  - Physical Review E
T1  - Influence of noise on dynamics of coupled bursters
VL  - 75
IS  - 6
DO  - 10.1103/PhysRevE.75.067204
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina and Vasović, Nebojša",
year = "2007",
abstract = "The influence of white noise on the dynamics of a delayed electrically coupled pair of Hidmarsh-Rose bursting neurons is studied. In particular a simple method to predict the intensity of noise that can destabilize the quiescent state is proposed and compared with numerical computations. Furthermore, it is demonstrated that quite small noise completely destroys the exact synchronization of bursting dynamics, and a qualitative explanation of this effect is discussed.",
publisher = "Amer Physical Soc, College Pk",
journal = "Physical Review E",
title = "Influence of noise on dynamics of coupled bursters",
volume = "75",
number = "6",
doi = "10.1103/PhysRevE.75.067204"
}

Burić, N., Todorović, K.,& Vasović, N.. (2007). Influence of noise on dynamics of coupled bursters. in Physical Review E
Amer Physical Soc, College Pk., 75(6).
https://doi.org/10.1103/PhysRevE.75.067204

Burić N, Todorović K, Vasović N. Influence of noise on dynamics of coupled bursters. in Physical Review E. 2007;75(6).
doi:10.1103/PhysRevE.75.067204 .

Burić, Nikola, Todorović, Kristina, Vasović, Nebojša, "Influence of noise on dynamics of coupled bursters" in Physical Review E, 75, no. 6 (2007),
https://doi.org/10.1103/PhysRevE.75.067204 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Ranković, Dragana
PY  - 2007
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/915
AB  - A pair of Hindmarsh-Rose neurons with delayed coupling is studied. Bifurcations due to time-lag and coupling and stability of the stationary state that corresponds to the quiescence behavior are analyzed. Bursting is created by coupling and its properties strongly depend on the time-lag. In particular, there is a domain of values of time-lags which renders the bursting of the two neurons exactly synchronous.
PB  - Elsevier Science BV, Amsterdam
T2  - Physics Letters A
T1  - Bursting neurons with coupling delays
VL  - 363
IS  - 4
SP  - 282
EP  - 289
DO  - 10.1016/j.physleta.2006.11.032
ER  - 

@article{
author = "Burić, Nikola and Ranković, Dragana",
year = "2007",
abstract = "A pair of Hindmarsh-Rose neurons with delayed coupling is studied. Bifurcations due to time-lag and coupling and stability of the stationary state that corresponds to the quiescence behavior are analyzed. Bursting is created by coupling and its properties strongly depend on the time-lag. In particular, there is a domain of values of time-lags which renders the bursting of the two neurons exactly synchronous.",
publisher = "Elsevier Science BV, Amsterdam",
journal = "Physics Letters A",
title = "Bursting neurons with coupling delays",
volume = "363",
number = "4",
pages = "282-289",
doi = "10.1016/j.physleta.2006.11.032"
}

Burić, N.,& Ranković, D.. (2007). Bursting neurons with coupling delays. in Physics Letters A
Elsevier Science BV, Amsterdam., 363(4), 282-289.
https://doi.org/10.1016/j.physleta.2006.11.032

Burić N, Ranković D. Bursting neurons with coupling delays. in Physics Letters A. 2007;363(4):282-289.
doi:10.1016/j.physleta.2006.11.032 .

Burić, Nikola, Ranković, Dragana, "Bursting neurons with coupling delays" in Physics Letters A, 363, no. 4 (2007):282-289,
https://doi.org/10.1016/j.physleta.2006.11.032 . .

TY  - JOUR
AU  - Burić, Nikola
AU  - Todorović, Kristina
PY  - 2006
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/688
AB  - Synchronization patterns in chains of N bi-directionally delayed coupled systems with delayed feedback are studied. Each system is hyperchaotic when decoupled from the chain. It is shown that chains with odd or even number of cites N display different spatial patterns of stable exact synchronization. When N is odd the only stable pattern of exact synchronization is between all of the units. When N is even, next to the nearest neighbors could become exactly synchronized, with the dynamics of the nearest neighbors related in a more complicated way. Sufficiently strong coupling leads to the nearest neighbor synchronization also for even N. No other patterns have been observed.
PB  - World Scientific Publ Co Pte Ltd, Singapore
T2  - International Journal of Bifurcation and Chaos
T1  - Patterns of exact synchronization in chains of feedback loops with two characteristic time-lags
VL  - 16
IS  - 5
SP  - 1569
EP  - 1584
DO  - 10.1142/S0218127406015519
ER  - 

@article{
author = "Burić, Nikola and Todorović, Kristina",
year = "2006",
abstract = "Synchronization patterns in chains of N bi-directionally delayed coupled systems with delayed feedback are studied. Each system is hyperchaotic when decoupled from the chain. It is shown that chains with odd or even number of cites N display different spatial patterns of stable exact synchronization. When N is odd the only stable pattern of exact synchronization is between all of the units. When N is even, next to the nearest neighbors could become exactly synchronized, with the dynamics of the nearest neighbors related in a more complicated way. Sufficiently strong coupling leads to the nearest neighbor synchronization also for even N. No other patterns have been observed.",
publisher = "World Scientific Publ Co Pte Ltd, Singapore",
journal = "International Journal of Bifurcation and Chaos",
title = "Patterns of exact synchronization in chains of feedback loops with two characteristic time-lags",
volume = "16",
number = "5",
pages = "1569-1584",
doi = "10.1142/S0218127406015519"
}

Burić, N.,& Todorović, K.. (2006). Patterns of exact synchronization in chains of feedback loops with two characteristic time-lags. in International Journal of Bifurcation and Chaos
World Scientific Publ Co Pte Ltd, Singapore., 16(5), 1569-1584.
https://doi.org/10.1142/S0218127406015519

Burić N, Todorović K. Patterns of exact synchronization in chains of feedback loops with two characteristic time-lags. in International Journal of Bifurcation and Chaos. 2006;16(5):1569-1584.
doi:10.1142/S0218127406015519 .

Burić, Nikola, Todorović, Kristina, "Patterns of exact synchronization in chains of feedback loops with two characteristic time-lags" in International Journal of Bifurcation and Chaos, 16, no. 5 (2006):1569-1584,
https://doi.org/10.1142/S0218127406015519 . .

TY  - JOUR
AU  - Aleksić, Mara
AU  - Savić, Vladimir
AU  - Popović, Gordana
AU  - Burić, Nikola
AU  - Kapetanović, Vera
PY  - 2005
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/616
AB  - Ionization constants of three cephalosporin antibiotics, cefetamet (CEF), cefotaxime (CFX) and ceftriaxone (CFTR) are determined using pH-potentiometric titrations at I= 0.1 M (NaCl) and t = 25 degrees C. Cefetarnet and cefotaxime have three ionization groups: carboxylic, amide and aminothiazole. Besides those three, ceftriaxone possesses an hydroxytriazi none group as new and additional ionization center. In acid medium two overlapping acid-base processes are occuring with acidity constants being: pK(1) 2.93 (COOH) and PK2 3.07 (amin nothiazole) for cefetamet, and pK(1) 2.21 (COOH) and pK(2) 3.15 (aminothiazole) for cefotaxime. In the case of ceftriaxone the situation is even more complicated, three overlapping processes coexist with pK(1) 2.37 (COOH), pK(2) 3.03 (aminothiazole) and pK(3) 4.21 (hydroxytriazinone). Protolysis of amide group is happening in the alkaline medium as completely separated process from those in acid medium. The acidity constants which correspond to amide group are pK(3) 10.65 (CEF), pK(3) 10.87 (CFX) and pK(4) 10.74 (CFTR). The influence of the C3 substituent on the dissociation process of the neighboring ionization group, particularly carboxylic group, was considered. The differences in acidity of CEF, CFX and CFFR pK(1): 2.93, 2.21 and 2.37, respectively) are likely to be caused by the stereoelectronic properties of substituents in the P-position to the carboxylic group due to the combined inductive, hyperconjugative and resonance effects.
PB  - Elsevier Science BV, Amsterdam
T2  - Journal of Pharmaceutical and Biomedical Analysis
T1  - Acidity constants of cefetamet, cefotaxime and ceftriaxone; the effect of the substituent at C3 position
VL  - 39
IS  - 3-4
SP  - 752
EP  - 756
DO  - 10.1016/j.jpba.2005.04.033
ER  - 

@article{
author = "Aleksić, Mara and Savić, Vladimir and Popović, Gordana and Burić, Nikola and Kapetanović, Vera",
year = "2005",
abstract = "Ionization constants of three cephalosporin antibiotics, cefetamet (CEF), cefotaxime (CFX) and ceftriaxone (CFTR) are determined using pH-potentiometric titrations at I= 0.1 M (NaCl) and t = 25 degrees C. Cefetarnet and cefotaxime have three ionization groups: carboxylic, amide and aminothiazole. Besides those three, ceftriaxone possesses an hydroxytriazi none group as new and additional ionization center. In acid medium two overlapping acid-base processes are occuring with acidity constants being: pK(1) 2.93 (COOH) and PK2 3.07 (amin nothiazole) for cefetamet, and pK(1) 2.21 (COOH) and pK(2) 3.15 (aminothiazole) for cefotaxime. In the case of ceftriaxone the situation is even more complicated, three overlapping processes coexist with pK(1) 2.37 (COOH), pK(2) 3.03 (aminothiazole) and pK(3) 4.21 (hydroxytriazinone). Protolysis of amide group is happening in the alkaline medium as completely separated process from those in acid medium. The acidity constants which correspond to amide group are pK(3) 10.65 (CEF), pK(3) 10.87 (CFX) and pK(4) 10.74 (CFTR). The influence of the C3 substituent on the dissociation process of the neighboring ionization group, particularly carboxylic group, was considered. The differences in acidity of CEF, CFX and CFFR pK(1): 2.93, 2.21 and 2.37, respectively) are likely to be caused by the stereoelectronic properties of substituents in the P-position to the carboxylic group due to the combined inductive, hyperconjugative and resonance effects.",
publisher = "Elsevier Science BV, Amsterdam",
journal = "Journal of Pharmaceutical and Biomedical Analysis",
title = "Acidity constants of cefetamet, cefotaxime and ceftriaxone; the effect of the substituent at C3 position",
volume = "39",
number = "3-4",
pages = "752-756",
doi = "10.1016/j.jpba.2005.04.033"
}

Aleksić, M., Savić, V., Popović, G., Burić, N.,& Kapetanović, V.. (2005). Acidity constants of cefetamet, cefotaxime and ceftriaxone; the effect of the substituent at C3 position. in Journal of Pharmaceutical and Biomedical Analysis
Elsevier Science BV, Amsterdam., 39(3-4), 752-756.
https://doi.org/10.1016/j.jpba.2005.04.033

Aleksić M, Savić V, Popović G, Burić N, Kapetanović V. Acidity constants of cefetamet, cefotaxime and ceftriaxone; the effect of the substituent at C3 position. in Journal of Pharmaceutical and Biomedical Analysis. 2005;39(3-4):752-756.
doi:10.1016/j.jpba.2005.04.033 .

Aleksić, Mara, Savić, Vladimir, Popović, Gordana, Burić, Nikola, Kapetanović, Vera, "Acidity constants of cefetamet, cefotaxime and ceftriaxone; the effect of the substituent at C3 position" in Journal of Pharmaceutical and Biomedical Analysis, 39, no. 3-4 (2005):752-756,
https://doi.org/10.1016/j.jpba.2005.04.033 . .