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Hyperbolic Chaos in Systems Based on FitzHugh – Nagumo Model Neurons

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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.

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Authors and Affiliations

  1. Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia

    Sergey P. Kuznetsov & Yuliya V. Sedova

  2. Udmurt State University, ul. Universitetskay 1, Izhevsk, 426034, Russia

    Sergey P. Kuznetsov

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  1. Sergey P. Kuznetsov
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  2. Yuliya V. Sedova
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Correspondence to Sergey P. Kuznetsov.

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Kuznetsov, S.P., Sedova, Y.V. Hyperbolic Chaos in Systems Based on FitzHugh – Nagumo Model Neurons. Regul. Chaot. Dyn. 23, 458–470 (2018). https://doi.org/10.1134/S1560354718040068

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

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