Pattern formation (II): The Turing Instability

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 $ln(1/\delta)$, where &\delta$ is the strength of the initial perturbation.