E3S Web Conf.
Volume 62, 2018IX International Conference “Solar-Terrestrial Relations and Physics of Earthquake Precursors”
|Number of page(s)||6|
|Section||Geophysical Fields and their Interactions|
|Published online||07 November 2018|
The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo
1 Vitus Bering Kamchatka State University, 683032, Kamchatskiy kray, Petropavlovsk - Kamchatskiy, Pogranichaya str. 4, Russia
2 Institute of Cosmophysical Research and Radio Wave Propagation of the Far Eastern Branch of Russian Academy of Science, 684034, Kamchatskiy kray, Paratunka, Mirnaya str. 7, Russia
In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), 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 and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. 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.
© The Authors, published by EDP Sciences, 2018
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