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This article is cited in 1 scientific paper (total in 1 paper)
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:
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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
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\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
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S. P. Kuznetsov, Yu. V. Sedova, “Giperbolicheskii khaos v ostsillyatore Bonkhoffera–van der Polya s dopolnitelnoi zapazdyvayuschei obratnoi svyazyu i periodicheski moduliruemym parametrom vozbuzhdeniya”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 27:1 (2019), 77–95
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