Bifurcations in Morris-Lecar neuron model

Authors:
Kunichika Tsumoto;Hiroyuki Kitajima;Tetsuya Yoshinaga;Kazuyuki Aihara;Hiroshi Kawakami
Affiliations:
Department of Telecommunications, Takuma National College of Technology, 551 Koda, Takuma, Kagawa 769-1192, Japan and Aihara Complexity Modelling Project, ERATO, Japan Science and Technology Agenc ...;Department of Reliability-based Information Systems Engineering, Faculty of Engineering, Kagawa University, 2217-20, Hayashi-cho, Takamatsu 761-0396, Japan;Department of Radiologic Science and Engineering, School of Health Sciences, The University of Tokushima, Tokushima, 3-18-15 Kuramoto, Tokushima 770-8509, Japan;Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo 153-8505, Japan and Aihara Complexity Modelling Project, ERATO, Japan Science and Technology Agency (JST), 3 ...;The University of Tokushima, 2-24, Shinkura, Tokushima 770-8501, Japan
Venue:
Neurocomputing
Year:
2006

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Abstract

The Morris-Lecar (M-L) equations are an important neuron model that exhibits classes I and II excitabilities when system parameters are set appropriately. Although many papers have clarified characteristic behaviors of the model, the detailed transition between two classes is unclear from the viewpoint of bifurcation analyses. In this paper, we investigate bifurcations of invariant sets in a five-dimensional parameter space, and identify an essential parameter of the half-activated potential of the potassium activation curve that contributes to the alternation of the membrane properties of the M-L neuron. We also show that the membrane property can be controlled by varying the value of the single parameter.