American Institute of Mathematical Sciences

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2011, 2011(Special): 391-399. doi: 10.3934/proc.2011.2011.391

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

Lixia Duan 1, , Dehong Zhai 1, and  Qishao Lu 2,

1. 

College of Science, North China University of Technology, Beijing 100144, China
2. 

Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received  July 2010 Revised  May 2011 Published  October 2011

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: neuronal model, Bifurcation, bursting, fast-slow dynamical analysis.
Mathematics Subject Classification: Primary: 34C15; Secondary: 92C20.
Citation: Lixia Duan, Dehong Zhai, Qishao Lu. Bifurcation and bursting in Morris-Lecar model for class I and class II excitability. Conference Publications, 2011, 2011 (Special) : 391-399. doi: 10.3934/proc.2011.2011.391
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