Self-organized pulse generator in a reaction-diffusion system

Abstract

We carry out computer simulations of a Bonhoeffer--van der Pol-type reaction-diffusion equation to study the properties of propagating pulses and their collision. By choosing a suitable nonlinearity where a stable limit cycle solution coexists with an equilibrium uniform solution, it is shown that two pulses propagating to the opposite directions do not annihilate upon collision but generate a localized domain which persistently emits pulses traveling outward. The stability of the localized domain and the propagating pulses are explored numerically.