`a`

Bifurcation and bursting in Morris-Lecar model for class I and class II excitability

Pages: 391 - 399, Issue Special, September 2011

 Abstract        Full Text (933.5K)              

Lixia Duan - College of Science, North China University of Technology, Beijing 100144, China (email)
Dehong Zhai - College of Science, North China University of Technology, Beijing 100144, China (email)
Qishao Lu - Department of Dynamics and Control, Beihang University, Beijing 100191, China (email)

Abstract: In this paper, we study and classify the firing patterns in the Morris-Lecar neuronal model with current-feedback (MLF) control. The Morris-Lecar model has two different types of neuronal excitability (i.e. class I and class II excitability) when the parameters are set appropriately. It is shown that the MLF model exhibits two types of bursting oscillations under the parameter set for class I while exhibits five types of bursting oscillations under the parameter set for class II. Furthermore, we study the relationship between the excitability and bursting oscillations by the two-parameter bifurcation analysis of the fast subsystem for class I and class II excitability, respectively. It shows that different bifurcation structures of the fast subsystem may lead to various types of bursting oscillations in the neuronal model.

Keywords:  Bifurcation, fast-slow dynamical analysis, neuronal model, bursting
Mathematics Subject Classification:  Primary: 34C15; Secondary: 92C20

Received: July 2010;      Revised: May 2011;      Published: October 2011.