Meeting of Chemical Wave Fronts Creates Chaos

Abstract

We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some initial positions chaos occurs and for others it does not. In a space-homogeneous system, we need at least three fronts to create time-periodic behaviour, while to create chaos, we should have four fronts. We also provide a short review of previously known results, and different known mechanisms of chaos generation for reaction–diffusion systems. Our results can be used for pattern coding, in particular, for morphogenesis.