Turing patterns in the Lengyel-Epstein system for the CIMA reaction

Wei Ming Ni, Moxun Tang

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127 Scopus citations


The first experimental evidence of the Turing pattern was observed by De Kepper and her associates (1990) on the CIMA reaction in an open unstirred gel reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. In this paper we report some fundamental analytic properties of the Lengyel-Epstein system. Our result also indicates that if either of the initial concentrations of the reactants, the size of the reactor, or the effective diffusion rate, are not large enough, then the system does not admit nonconstant steady states. A priori estimates are fundamental to our approach for this nonexistence result. The degree theory was combined with the a priori estimates to derive existence of nonconstant steady states.

Original languageEnglish (US)
Pages (from-to)3953-3969
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - Oct 2005


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