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  - Kostić, Srdan
AU  - Franović, Igor
AU  - Perc, Matjaz
AU  - Vasović, Nebojša
AU  - Todorović, Kristina
PY  - 2014
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2206
AB  - The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic-or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale.
PB  - Nature Publishing Group, London
T2  - Scientific World Journal
T1  - Triggered dynamics in a model of different fault creep regimes
VL  - 4
DO  - 10.1038/srep05401
ER  - 

@article{
author = "Kostić, Srdan and Franović, Igor and Perc, Matjaz and Vasović, Nebojša and Todorović, Kristina",
year = "2014",
abstract = "The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic-or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale.",
publisher = "Nature Publishing Group, London",
journal = "Scientific World Journal",
title = "Triggered dynamics in a model of different fault creep regimes",
volume = "4",
doi = "10.1038/srep05401"
}

Kostić, S., Franović, I., Perc, M., Vasović, N.,& Todorović, K.. (2014). Triggered dynamics in a model of different fault creep regimes. in Scientific World Journal
Nature Publishing Group, London., 4.
https://doi.org/10.1038/srep05401

Kostić S, Franović I, Perc M, Vasović N, Todorović K. Triggered dynamics in a model of different fault creep regimes. in Scientific World Journal. 2014;4.
doi:10.1038/srep05401 .

Kostić, Srdan, Franović, Igor, Perc, Matjaz, Vasović, Nebojša, Todorović, Kristina, "Triggered dynamics in a model of different fault creep regimes" in Scientific World Journal, 4 (2014),
https://doi.org/10.1038/srep05401 . .