ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Cite this article as:

Feoktistov A. V., Anishenko V. S. Dynamics of the fitzhugh–nagumo system under external periodic force. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 5, pp. 35-44. DOI: https://doi.org/10.18500/0869-6632-2011-19-5-35-44

Language: 
Russian

Dynamics of the fitzhugh–nagumo system under external periodic force

Autors: 
Feoktistov Aleksej Vladimirovich, Saratov State University
Anishenko Vadim Semenovich, Saratov State University
Abstract: 

In paper on basis of radiophysical experiment analysis of dynamics of the FitzHugh–Nagumo system have been carried out. The dependence of oscillation’s regime in the system from force parameter has been found out. In?uence of the form of the external force signal on the system response has been studied.

Key words: 
DOI: 
10.18500/0869-6632-2011-19-5-35-44
References: 

1. Yanagita T., Nishiura Y., Kobayashi R. Signal propagation and failure in one-dimensional FitzHugh–Nagumo equations with periodic stimuli // Phys. Rev. E. 2005. Vol. 71. 036226. 2. Gong P.-L., Xu J.-X. Global dynamics and stochastic resonance of the forced Fitz-Hugh–Nagumo neuron model // Phys. Rev. E. 2001. Vol. 63. 031906. 3. Coombes S., Osbaldestin A.H. Period-adding bifurcation and chaos in periodically stimulated excitable neural relaxation oscillator // Phys. Rev. E. 2000. Vol. 62, No 3. P. 4057. 4. Othmer H.G., Xie M. Subharmonic resonance and chaos in forced excitable systems // J. Math. Biol. 2006. Vol. 39. P. 139. 5. Lee S.-G., Seunghwan K. Bifurcation analysis of mode-locking structure in a Hodgkin–Huxley neuron under sinusoidal current // Phys. Rev. E. 2006. Vol. 73. 041924. 6. Alexander J.C., Doedel E.J., Othmer H.G. . On the resonance structure in a forced excitable system // SIAM J. Appl. Math. 1990. Vol. 50, No 5. P. 1373. 7. Pikovsky A.S., Kurths Ju. Coherence resonance in a noise-driven excitable system // Phys. Rev. Lett. 1997. Vol. 78. P. 775. 8. Linder B., Schimansky-Geier L. Analitical approach to the stochastic FitzHugh–Nagumo system and coherence resonance // Phys. Rev. E. 1999. Vol. 60, No 6. P. 7270. 9. Феоктистов А.В., Астахов С.В., Анищенко В.С. Когерентный резонанс и синхронизация стохастических автоколебаний в системе ФитцХью–Нагумо // Изв. вузов. Прикладная нелинейная динамика. 2010. Т. 18, No 5. 10. Croisier H. Continuation and bifurcation analyses of a periodically forced slow–fast system. Liege, Mars. 2009. 11. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane // Bull. Math. Biophysics. 1955. Vol. 17. P. 257. 12. Андронов А.А., Витт А.А., Хайкин С.Э. Теория колебаний. М.: Наука, 1981. 13. Эрроусмит Д., Плейс К. Обыкновенные дифференциальные уравнения. Качественная теория с приложениями: Пер. с англ. М.: Мир, 1986. 243 с. 14. Izhikevich E.M. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press, Cambridge, MA, 2007.  

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