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

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 model
• traveling waves
• solitary wave solutions
• homoclinic orbits
• fitzhugh-nagumo equation