Complicated dynamics of a ring of nonidentical FitzHugh-Nagumo neurons with delayed couplings.

*(English)*Zbl 1373.34112Summary: This paper focuses on the dynamical properties of a ring FitzHugh-Nagumo neural network with delayed couplings. The stability switches of the network equilibrium are analyzed, and the sufficient conditions for the existence of the periodic oscillations are given. Case studies of numerical simulations are performed to validate the analytical results and to explore interesting dynamical properties. Complicated behaviors of the coupled network are observed, such as multiple switches between the rest states and periodic oscillations, the coexistence of different periodic oscillations, and chaotic attractors. It is shown that both coupling strengths and time delays play important roles in the network dynamics, such as period-doubling bifurcation leading to chaos.

##### MSC:

34K23 | Complex (chaotic) behavior of solutions to functional-differential equations |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

34K20 | Stability theory of functional-differential equations |

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