A simple method of parameter space determination for diffusion-driven instability with three species (Q5938934)

The authors deal with the reaction diffusion system of the form NEWLINE\[NEWLINE\begin{aligned} {\partial u\over\partial t} & = f(u,v,w)+ d_1\nabla^2u,\\ {\partial v\over\partial t} & = g(u,v,w)+ d_2\nabla^2 u,\tag{1}\\ {\partial w\over\partial t} & = h(u,v,w)+ d_3\nabla^2u,\end{aligned}NEWLINE\]NEWLINE 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.