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Regul. Chaotic Dyn., 2018, Volume 23, Issue 4, Pages 458–470 (Mi rcd333)  

Hyperbolic Chaos in Systems Based on FitzHugh–Nagumo Model Neurons

Sergey P. Kuznetsovab, Yuliya V. Sedovab

a Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia
b Udmurt State University, ul. Universitetskay 1, Izhevsk, 426034 Russia

Abstract: In the present paper we consider and study numerically two systems based on model FitzHugh–Nagumo neurons, where in the presence of periodic modulation of parameters it is possible to implement chaotic dynamics on the attractor in the form of a Smale–Williams solenoid in the stroboscopic Poincaré map. In particular, hyperbolic chaos characterized by structural stability occurs in a single neuron supplemented by a time-delay feedback loop with a quadratic nonlinear element.

Keywords: hyperbolic chaos, Smale–Williams solenoid, FitzHugh–Nagumo neuron, time-delay system

Funding Agency Grant Number
Russian Science Foundation 17-12-01008
This work was supported by the Russian Science Foundation (grant No 17-12-01008).


DOI: https://doi.org/10.1134/S1560354718040068

References: PDF file   HTML file

Bibliographic databases:

MSC: 37D05, 37D20, 37D45, 37M25, 82C32, 92B20
Received: 06.05.2018
Accepted:04.06.2018
Language:

Citation: Sergey P. Kuznetsov, Yuliya V. Sedova, “Hyperbolic Chaos in Systems Based on FitzHugh–Nagumo Model Neurons”, Regul. Chaotic Dyn., 23:4 (2018), 458–470

Citation in format AMSBIB
\Bibitem{KuzSed18}
\by Sergey P. Kuznetsov, Yuliya V. Sedova
\paper Hyperbolic Chaos in Systems Based on FitzHugh–Nagumo Model Neurons
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 4
\pages 458--470
\mathnet{http://mi.mathnet.ru/rcd333}
\crossref{https://doi.org/10.1134/S1560354718040068}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3836281}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85051109741}


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