# American Institute of Mathematical Sciences

January  2012, 11(1): 189-207. doi: 10.3934/cpaa.2012.11.189

## An effective design method to produce stationary chemical reaction-diffusion patterns

 1 Centre De Recherche Paul Pascal, CNRS, Av. Schweitzer, 33600 Pessac, France 2 Institute of Chemistry, Laboratory of Nonlinear Chemical Dyanmics, Eötvös L. University, P.O. Box H-1518 Budapest 112, Hungary

Received  March 2010 Revised  July 2010 Published  September 2010

We present a semi-empirical experimental design method to produce nontrivial chemical reaction-diffusion patterns in open reactors. We specially focus on the development of stationary patterns. The method is based on autoactivated reactions that produces spatial bistability, the addition of an independent antagonist reaction to produce spatio-temporal oscillations, and the introduction of a low mobility complexing agent that rapidly and reversibly binds the main autoactivatory species. The method is presented in formal way. Actual experimental results are used for illustration. We point out the open problems of the mathematical description: they relate to the boundary conditions, to the dimensionality of the system, and to the coupled time- and space-scale changes induced by the complexing agent.
Citation: Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure & Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189
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