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A simple method of parameter space determination for diffusion-driven instability with three species. (English) Zbl 0980.35062

The authors deal with the reaction diffusion system of the form \[ \begin{aligned} {\partial u\over\partial t} & = f(u,v,w)+ d_1\nabla^2u,\\ {\partial v\over\partial t} & = g(u,v,w)+ d_2\nabla^2 u,\tag{1}\\ {\partial w\over\partial t} & = h(u,v,w)+ d_3\nabla^2u,\end{aligned} \] where \(f\), \(g\) and \(h\) represent nonlinear kinetics, and \(d_1\), \(d_2\) and \(d_3\) are the respective diffusion coefficients of \(u\), \(v\) and \(w\). They derive very simple, practical criteria for diffusion-driven linear instability and parameter space determination for (1). As an example of applications they deal with the three-species Oregonator and the Belousov-Zhabotinsky reaction.

MSC:

35K55 Nonlinear parabolic equations
35K40 Second-order parabolic systems
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
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