Selection and competition of Turing patterns

Abstract

We examine the selection and competition of patterns in the Brusselator model, one of the simplest reaction-diffusion systems giving rise to Turing instabilities. Simulations of this model show a significant change in the wave number of stable patterns as the control parameter is increased. A weakly nonlinear analysis makes it possible to obtain the amplitude equations for the concentration fields near the instability threshold. Together with the linear diffusive terms, these equations also contain nonvariational spatial terms. When these terms are included, the stability diagrams and the thresholds for secondary instabilities are heavily modified with respect to the usual diffusive case. The results obtained from the numerical simulations fit very well into the calculated stability regions.