Delay-induced instability and oscillations in a multiplex neural system with Fitzhugh-Nagumo networks

Weijie Ding; Xiaochen Mao; Lei Qiao; Mingjie Guan; Minqiang Shao; Weijie Ding; Xiaochen Mao; Lei Qiao; Mingjie Guan; Minqiang Shao

doi:10.3934/era.2022057

Electronic Research Archive

2022, Volume 30, Issue 3: 1075-1086. doi: 10.3934/era.2022057

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Delay-induced instability and oscillations in a multiplex neural system with Fitzhugh-Nagumo networks

1.
Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, China
2.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received: 14 October 2021 Revised: 16 November 2021 Accepted: 16 November 2021 Published: 11 March 2022

In this paper, we study the nonlinear dynamics of a multiplex system consisting of neuronal networks each with an arbitrary number of FitzHugh-Nagumo neurons and intra-connections and delayed couplings. The network contains an autaptic connection formed by the axon of a neuron on its own soma or dendrites. The stability and instability of the network are determined and the existence of bifurcation is discussed. Then, the study turns to validate the theoretical analysis through numerical simulations. Abundant dynamical phenomena of the network are explored, such as coexisting multi-period oscillations and chaotic responses.
- neuronal networks,
- time delays,
- multiplex structure,
- complexity
Citation: Weijie Ding, Xiaochen Mao, Lei Qiao, Mingjie Guan, Minqiang Shao. Delay-induced instability and oscillations in a multiplex neural system with Fitzhugh-Nagumo networks[J]. Electronic Research Archive, 2022, 30(3): 1075-1086. doi: 10.3934/era.2022057

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Abstract

In this paper, we study the nonlinear dynamics of a multiplex system consisting of neuronal networks each with an arbitrary number of FitzHugh-Nagumo neurons and intra-connections and delayed couplings. The network contains an autaptic connection formed by the axon of a neuron on its own soma or dendrites. The stability and instability of the network are determined and the existence of bifurcation is discussed. Then, the study turns to validate the theoretical analysis through numerical simulations. Abundant dynamical phenomena of the network are explored, such as coexisting multi-period oscillations and chaotic responses.

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