Pattern formation (II): The Turing Instability

Abstract

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the finite number of linear growing modes over a time scale of ln ⁡ 1 δ , \ln \frac {1}{\delta }, where δ \delta is the strength of the initial perturbation.