Collision-Stable Waves in Excitable Reaction-Diffusion Systems

Abstract

We discuss the interaction of stable pulse solutions modeling reduction waves in the Belousov-Zhabotinsky reaction in a spatially one-dimensional reaction-diffusion system. We find that in the range of parameters close to a subcritical Hopf bifurcation the counterpropagating pulses do not annihilate in a collision but emerge after the collision with a size and shape unchanged compared to those well before the collision. Under similar conditions these pulse solutions are reflected at zero-flux surfaces (“echo waves”).