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

Feifei Cheng; Ji Li; Qing Yu; Feifei Cheng; Ji Li; Qing Yu

doi:10.3934/math.2023171

AIMS Mathematics

2023, Volume 8, Issue 2: 3322-3337. doi: 10.3934/math.2023171

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Research article

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

Feifei Cheng ¹,
Ji Li ^{2
,
,},
Qing Yu ²

1.
Department of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan, Henan 467036, China
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Received: 26 August 2022 Revised: 01 November 2022 Accepted: 07 November 2022 Published: 17 November 2022
MSC : 35C07, 35C08, 37C29

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.
- neuron model,
- traveling waves,
- solitary wave solutions,
- homoclinic orbits,
- FitzHugh-Nagumo equation
Citation: Feifei Cheng, Ji Li, Qing Yu. The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry[J]. AIMS Mathematics, 2023, 8(2): 3322-3337. doi: 10.3934/math.2023171

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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.

References

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