COHERENCE RESONANCE AND SYNCHRONIZATION OF STOCHASTIC SELF-SUSTAINED OSCILLATIONS IN THE FITZHUGH–NAGUMO SYSTEM


Cite this article as:

Feoktistov А. V., Astakhov S. V., Anishenko V. S. COHERENCE RESONANCE AND SYNCHRONIZATION OF STOCHASTIC SELF-SUSTAINED OSCILLATIONS IN THE FITZHUGH–NAGUMO SYSTEM. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 5, pp. 33-43. DOI: https://doi.org/10.18500/0869-6632-2010-18-5-33-43


In present paper the phenomena of coherence resonance, mutual and external synchronization of noise-induced stochastic oscillations in FitzHugh–Nagumo system are studied by means of numerical and natural experiments. The properties of attractor in the system as well as energy exchange processes are analyzed. Self-sustained character of stochastic oscillations in non-autonomous FitzHugh–Nagumo system justified.

DOI: 
10.18500/0869-6632-2010-18-5-33-43
Literature

1. Pikovsky A.S. and Kurths J. Coherence resonance in a noise-driven excitable system // Phys. Rev. Lett. 1997. Vol. 78. P. 775.

2. Linder B., Schimansky-Geier L. Analytical approach to the stochastic FitzHugh–Nagumo system and coherence resonance // Phys. Rev. E. 1999. Vol. 60, No 6. P. 7270.

3. Izhikevich E.M. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press. Cambridge. MA, 2007.

4. FitzHugh R. Mathematical models of threshold phenomena in the nerve membrane // Bull. Math. Biophysics. 1955. Vol. 17. P. 257.

5. Scott A.C. The electrophysics of a nerve fiber // Rev. Mod. Phys. 1975. Vol. 47. P. 487.

6. Longtin A. Stochastic resonance in neuron models // J. Stat. Phys. 1993. Vol. 70. P. 309.

7. Baltanas J.P., Casado J.M. Bursting behaviour of the FitzHugh–Nagumo neuron model subject to quasi-monochromatic noise // Phys. D. 1998. Vol. 122, No 1. P. 231.

8. Han S.K., Yim T.G., Postnov D.E., Sosnovtseva O.V. Interacting coherence resonance oscillators // Phys. Rev. Lett. 1999. Vol. 83, No 9. P. 1771.

9. Neiman A., Schimansky-Geier L., Cornell-Bell A., Moss F. Noise-enhanced phase synchronization in excitable media // Phys. Rev. Lett. 1999. Vol. 83, No 23. P. 4896.

10. Hu B., Zhou Ch. Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance // Phys. Rev. E. 2000. Vol. 61, No 2. R1001- R1004.

11. Андронов А.А., Витт А.А., Хайкин С.Э. Теория колебаний. М.: Наука, 1981.

12. Makarov V.A., del Rio E., Ebeling W., and Velarde M.G. Dissipative Toda-Rayleigh lattice and its oscillatory modes // Phys. Rev. E. 2001. Vol. 64. 036601.

13. Анищенко В.С., Вадивасова Т.Е., Стрелкова Г.И. Автоколебания динамических и стохастических систем и их математический образ–аттрактор // Нелинейная динамика, 2010 (принята к публикации).

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Феоктистов -IzvVUZ_AND-18-5-33,
author = {А. V. Feoktistov and S. V. Astakhov and Vadim S. Anishenko},
title = {COHERENCE RESONANCE AND SYNCHRONIZATION OF STOCHASTIC SELF-SUSTAINED OSCILLATIONS IN THE FITZHUGH–NAGUMO SYSTEM},
year = {2010},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {18},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/coherence-resonance-and-synchronization-of-stochastic-self-sustained-oscillations-in-the},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2010-18-5-33-43},pages = {33--43},issn = {0869-6632},
keywords = {coherence resonance,synchronization,stochastic self-sustained oscillations,FitzHugh–Nagumo system,noise-induced oscillations.},
abstract = {In present paper the phenomena of coherence resonance, mutual and external synchronization of noise-induced stochastic oscillations in FitzHugh–Nagumo system are studied by means of numerical and natural experiments. The properties of attractor in the system as well as energy exchange processes are analyzed. Self-sustained character of stochastic oscillations in non-autonomous FitzHugh–Nagumo system justified. }}