Dynamical transitions of Turing patterns

Abstract

This paper is concerned with the formation and persistence of spatiotemporal patterns in binary mixtures of chemically reacting species, where one of the species is an activator, the other an inhibitor of the chemical reaction. The system of reaction–diffusion equations is reduced to a finite system of ordinary differential equations by a variant of the centre-manifold reduction method. The reduced system fully describes the local dynamics of the original system near transition points at the onset of instability. The attractor–bifurcation theory is used to give a complete characterization of the bifurcated objects in terms of the physical parameters of the problem. The results are illustrated for the Schnakenberg model.