Towards a global classification of excitable reaction-diffusion systems

Abstract

Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this paper we propose a global classification of two variable excitable reaction-diffusion systems. In particular, we claim that the topology of the underlying two-dimensional homogeneous dynamics organizes the system's behavior. We believe that this classification provides a useful tool for the modeling of any real system whose microscopic details are unknown. (C) 2000 Published by Elsevier Science B.V.