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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
DOI: https://doi.org/10.1134/S1560354718040068   References:
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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), 
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