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), where &\delta$ is the strength of the initial perturbation.
@article{arxiv.math/0510419,
title = {Pattern formation (II): The Turing Instability},
author = {Yan Guo and Hyung Ju Hwang},
journal= {arXiv preprint arXiv:math/0510419},
year = {2007}
}