Reaction–diffusion systems with fluctuating diffusivity; spatio-temporal chaos and phase separation

Abstract

The homogeneous stable state of a one-component reaction–diffusion system with positive diffusivity always remains stable by diffusion. We have shown that dichotomously fluctuating diffusivity leads to an instability of the stable state for an optimal range of correlation times of dichotomous noise. The instability condition corresponds to the rare event of instantaneous diffusivity remaining negative for typical realizations of dichotomous fluctuations over a finite correlation time. Detailed numerical simulations reveal that, depending on the characteristic non-linearity of the reaction term, this fluctuating diffusivity-driven instability results in irregular non-stationary patterns in the form of spatio-temporal chaos or phase-separation.