Pattern formation (II): The Turing Instability

Guo, Yan; Hwang, Hyung Ju

doi:10.1090/S0002-9939-07-08850-8

Pattern formation (II): The Turing Instability
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by Yan Guo and Hyung Ju Hwang PDF

Proc. Amer. Math. Soc. 135 (2007), 2855-2866 Request permission

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 $\ln \frac {1}{\delta },$ where $\delta$ is the strength of the initial perturbation.

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