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.