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Research Article | Open Access

The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry

Feifei Cheng1, Ji Li2( ), Qing Yu2
Department of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan, Henan 467036, China
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
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Abstract

The neuron model with conductance-resistance symmetry was recently derived by Deng, which is similar to the Hodgkin-Huxley equation, referred to as CRS neuron model. In this paper, we will consider a 2-dimensional reduction model qualitatively similar to the FitzHugh-Nagumo equation. We first give the derivation of the CRS neuron model in propagating action potential. And then we prove the existence of solitary wave solution for the 2-dimensional reduced CRS neuron model by using phase diagram analysis.

Keywords

neuron modeltraveling wavessolitary wave solutionshomoclinic orbitsFitzHugh-Nagumo equation
CLC number: 35C07, 35C08, 37C29

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 3322-3337
DOI: 10.3934/math.2023171

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Cite this article:
Cheng F, Li J, Yu Q. The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry. AIMS Mathematics, 2023, 8(2): 3322-3337. https://doi.org/10.3934/math.2023171

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Received: 26 August 2022
Revised: 01 November 2022
Accepted: 07 November 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)