Research article

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

  • 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.

    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

    Related Papers:

  • 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.



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