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

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Abstract

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.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 11472097, Fundamental Research Funds for the Central Universities under Grant No. 2015B18214, State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) under Grant No. MCMS-0113G01, China Scholarship Council, and Outstanding Innovative Talents Support Plan of Hohai University. The author thanks the anonymous reviewers and editor for helpful comments and suggestions that have helped to improve the presentation.

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Authors and Affiliations

  1. Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 210098, China

    Xiaochen Mao

  2. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xiaochen Mao

  3. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA

    Xiaochen Mao

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  1. Xiaochen Mao
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Mao, X. Complicated dynamics of a ring of nonidentical FitzHugh–Nagumo neurons with delayed couplings. Nonlinear Dyn 87, 2395–2406 (2017). https://doi.org/10.1007/s11071-016-3198-y

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  • DOI: https://doi.org/10.1007/s11071-016-3198-y

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