Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:B3L-A
Session:
Number:B3L-A3
Analyses of the dynamics of interconnected van der pol models based-on a concept of potential with active areas
Koji Kurose, Yoshihiro Hayakawa, Koji Nakajima,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
We present various bursting wave forms that are obtain from a simple model of Hodgkin-Huxley type. The model is a typical example whose characteristics can be discussed through a concept of potential with active areas. A potential function is able to provide a global landscape for dynamics of a model, and the dynamics are explained in relation to the disposition of the active area on the potential. We obtain the potential functions and the active areas for a Hindmarsh-Rose model,a Morris-Lecar system, and a Hodgkin-Huxley system, and hence we are able to discuss the common properties among these models based on the concept of potential with active areas. Furthermore, we are able to understand intuitively a bifurcation of an interconnected van der pol system by using the potential, so that the new concept is very useful to describe the dynamics of interconnected systems.