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Filippov FitzHugh-Nagumo Neuron Model with Membrane Potential Threshold Control Policy

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Abstract

In this paper, a novel FitzHugh-Nagumo (FHN) neuron model with membrane potential threshold control policy is proposed. As the membrane potential threshold control policy is a switching control policy, our proposed model is a Filippov system, which is different from the existing FHN model. For this model, first, the sliding segments and sliding regions are investigated. Then, based on the obtained sliding regions, we discuss the null-clines and the existence conditions of various equilibria such as regular equilibrium, virtual equilibrium and boundary equilibrium. By choosing the membrane potential threshold as the bifurcation parameter, the boundary node bifurcation, pseudo-saddle-node bifurcation and the global touching bifurcation are investigated by using numerical techniques. Furthermore, the effectiveness and correctness of the proposed FHN model with membrane potential threshold control policy are verified by circuit simulation. Numerical examples show that the membrane potential threshold guided switching may cause complex dynamics.

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Acknowledgements

This work was supported in part by the National Key Research and Development Project of China under Grant 2018AAA0100101, in part by Fundamental Research Funds for the Central Universities under Grant XDJK2020B009, in part by Chongqing Basic and Frontier Research Project under Grant cstc2019jcyj-msxmX0470, and cstc2020jcyj-msxmX0139, in part by the Chongqing Technological Innovation and Application Project under Grant cstc2018jszx-cyzdX0171, in part by the Science and Technology Research Program of Chongqing Municipal Education Commission under Grant KJQN201900816, in part by Chongqing Social Science Planning Project under Grant 2019BS053.

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  1. Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronics and Information Engineering, Southwest University, Chongqing, 400715, P.R. China

    Tao Dong & Huiyun Zhu

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  1. Tao Dong
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  2. Huiyun Zhu
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Correspondence to Tao Dong.

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Dong, T., Zhu, H. Filippov FitzHugh-Nagumo Neuron Model with Membrane Potential Threshold Control Policy. Neural Process Lett 53, 3801–3824 (2021). https://doi.org/10.1007/s11063-021-10549-z

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