Impact of Chloride Channel on Spiking Patterns of Morris-Lecar Model

Tahmineh Azizi,Bacim Alali

doi:10.4236/am.2020.117044

Abstract

In this paper,we study the complicated dynamics of general Morris-Lecar model with the impact of Cl- fluctuations on firing patterns of this neuron model. After adding Cl- channel in the original Morris-Lecar model, the dynamics of the original model such as its bifurcations of equilibrium points would be changed and they occurred at different values compared to the primary model. We discover these qualitative changes in the point of dynamical systems and neuroscience. We will conduct the co-dimension two bifurcations analysis with respect to different control parameters to explore the complicated behaviors for this new neuron model.

Highlights

Computational neuroscience uses knowledge of biology and combines with mathematical modeling to simulate the fluctuations of neuron cells and biological physiological characteristics of them [1] [2] [3] [4]
We study the complicated dynamics of general Morris-Lecar model with the impact of Cl− fluctuations on firing patterns of this neuron model
After adding Cl− channel in the original Morris-Lecar model, the dynamics of the original model such as its bifurcations of equilibrium points would be changed and they occurred at different values compared to the primary model

Summary

Introduction

Computational neuroscience uses knowledge of biology and combines with mathematical modeling to simulate the fluctuations of neuron cells and biological physiological characteristics of them [1] [2] [3] [4]. The Morris-Lecar model describes the electrical activities of neurons with a system of two nonlinear ordinary differential equations and includes different channels. This model reduces the four-dimensional Hodgkin-Huxley model to be a two-dimensional system of ordinary differential equations while keeping the major neuronal properties of generating action potential but through simpler mathematical model [11] [12] [13]. The general Morris-Lecar model includes three channels: a potassium channel, a leak and a calcium channel and has the following form [7]. We are interested to discover the co-dimension two bifurcations such as Bautin or generalized Hopf and Bogdanov-Takens and cusp bifurcations and we present the normal form of these bifurcations

Supercritical Hopf Bifurcation and Subcritical Hopf Bifurcation

The Homoclinic Case

Discussion and Conclusion