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 Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Issue 3(23), Pages 116–123 (Mi vkam262)

MATHEMATICAL MODELING OF DYNAMIC SYSTEMS

Investigation of regular and chaotic modes of the FitzHugh-Nagumo fractal oscillator

O. D. Lipko

Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia

Abstract: In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (EFN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure, the Lyapunov maximum exponent spectra were constructed as a function of the values of the control parameters of the model of the EFN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

Keywords: limit cycle, FitzHugh-Nagumo oscillator with power memory, the spectrum of Lyapunov maximum exponents, oscillograms and phase trajectories.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-1152.2018.1ÀÀÀÀ-À17-117031050058-9 This work was supported by the grant of the President of the Russian Federation No. MK-1152.2018.1 and on the topic of the research of Vitus Bering Kamchatka State University «Application of fractional calculus in the theory of oscillatory processes»No.ÀÀÀÀ-À17-117031050058-9.

DOI: https://doi.org/10.18454/2079-6641-2018-23-3-116-123

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Document Type: Article
UDC: 517.938
MSC: Primary 34A08; Secondary 34K28, 37N30

Citation: O. D. Lipko, “Investigation of regular and chaotic modes of the FitzHugh-Nagumo fractal oscillator”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 116–123

Citation in format AMSBIB
\Bibitem{Lip18} \by O.~D.~Lipko \paper Investigation of regular and chaotic modes of the FitzHugh-Nagumo fractal oscillator \jour Vestnik KRAUNC. Fiz.-Mat. Nauki \yr 2018 \issue 3(23) \pages 116--123 \mathnet{http://mi.mathnet.ru/vkam262} \crossref{https://doi.org/10.18454/2079-6641-2018-23-3-116-123}