Sustained Non-Equilibrium Patterns in a One-Dimensional Reaction-Diffusion Chemical System

Abstract

We present numerical evidence for the existence of non trivial spatio-temporal patterns in a one-dimensional reaction-diffusion chemical system, with equal diffusion coefficients. The main motivation for such a study is the fact that, besides the so-called target and spiral-wave patterns, there exists so far no unambiguous experimental evidence of nontrivial spatio-temporal patterns, resulting solely from the interaction between reaction and diffusion processes and not from convective or interfacial effects. According to a common belief, this situation arises because all the diffusion coefficients of the different chemical species are approximately equal under general experimental conditions. In fact, it can be shown that, in the limit of equal diffusion coefficients, the diffusion coupling cannot destabilize a stable homogeneous steady state. Our purpose is to show that one can overcome this difficulty when imposing concentration gradients to the system.