Back and forth invasion in the interaction of Turing and Hopf domains in a reactive microemulsion system

Abstract

Pattern formation is studied numerically for a reactive microemulsion when two parts of the system with different droplet fractions are initially put into contact. We analyze the resulting dynamics when the volume droplet fraction readjusts by diffusion. When both parts initially sustain Turing patterns, the whole system readjusts its wavelength to the one that corresponds to the mean droplet fraction. Similarly, when both subsystems initially display bulk oscillations, the system readjusts its temporal frequency to that of the mean droplet fraction. More surprisingly, when one of the subsystems shows Turing patterns, and the other bulk oscillations, there is a back and forth invasion of domains, the final pattern corresponding to the one of the mean droplet fraction.