Geodesic
Investigation of regular and chaotic modes of the FitzHugh-Nagumo fractal oscillator
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 116-123

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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. 
@article{VKAM_2018_3_a13,
     author = {O. D. Lipko},
     title = {Investigation of regular and chaotic modes of the {FitzHugh-Nagumo} fractal oscillator},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {116--123},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_3_a13/}
}
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O. D. Lipko. Investigation of regular and chaotic modes of the FitzHugh-Nagumo fractal oscillator. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 116-123. http://geodesic.mathdoc.fr/item/VKAM_2018_3_a13/