Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays
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 effec...ts 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.
Keywords:
Time-delay / Noise / Coherent spikingSource:
Communications in Nonlinear Science and Numerical Simulation, 2014, 19, 9, 3202-3219Publisher:
- Elsevier Science BV, Amsterdam
Funding / projects:
- Modeling and Numerical Simulations of Complex Many-Body Systems (RS-MESTD-Basic Research (BR or ON)-171017)
DOI: 10.1016/j.cnsns.2014.02.022
ISSN: 1007-5704
WoS: 000333450200028
Scopus: 2-s2.0-84897040661
Collections
Institution/Community
PharmacyTY - 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 . .