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Regular and Chaotic Dynamics

, Volume 23, Issue 4, pp 458–470 | Cite as

Hyperbolic Chaos in Systems Based on FitzHugh – Nagumo Model Neurons

  • Sergey P. Kuznetsov
  • Yuliya V. Sedova
Article

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 

MSC2010 numbers

37D05 37D20 37D45 37M25 82C32 92B20 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov BranchSaratovRussia
  2. 2.Udmurt State UniversityIzhevskRussia

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