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Vestnik KRAUNC. Fiz.-Mat. Nauki, 2019, Volume 26, Number 1, Pages 63–70 (Mi vkam342)  

MATHEMATICAL MODELING

Stability of the rest points fractional oscillator FitzHugh-Nagumo

O. D. Lipko

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

Abstract: In this paper, using the qualitative analysis, we studied the stability of the point of rest of the fractional oscillator FitzHugh-Nagumo in commensurate and incommensurable cases. For the corresponding point of rest, using the numerical method of the theory of finite difference schemes, phase trajectories were constructed. It is shown that quiescent points can be both asymptotically stable, which correspond to stable focus, and are asymptotically unstable (unstable focus), and for them the phase trajectories usually go to the limit cycle.

Keywords: rest points, stability, limit cycle, FitzHugh-Nagumo fractional oscillator, phase trajectories.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation جت-1152.2018.1
The work was supported by the grant of the President of the Russian Federation No. MK-1152.2018.


DOI: https://doi.org/10.26117/2079-6641-2019-26-1-63-70

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Full text: http://krasec.ru/lipko2019261/
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UDC: 512.24
MSC: 37N10
Received: 16.03.2019

Citation: O. D. Lipko, “Stability of the rest points fractional oscillator FitzHugh-Nagumo”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 26:1 (2019), 63–70

Citation in format AMSBIB
\Bibitem{Lip19}
\by O.~D.~Lipko
\paper Stability of the rest points fractional oscillator FitzHugh-Nagumo
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2019
\vol 26
\issue 1
\pages 63--70
\mathnet{http://mi.mathnet.ru/vkam342}
\crossref{https://doi.org/10.26117/2079-6641-2019-26-1-63-70}
\elib{https://elibrary.ru/item.asp?id=38190075}


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