Excitable media in open and closed chaotic flows

Abstract

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.