Spatio-temporal chaos for the Gray-Scott model (Q5940266)

The authors study the dynamic phase transition to a spatio-temporal chaos (STC) from a global bifurcation viewpoint of the following Gray-Scott model NEWLINE\[NEWLINE\partial u/\partial t= D_u\nabla^2 u- uv^2+ F(1-u),\;\partial v/\partial t= D_v\nabla^2 v+ uv^2- (F+ k)v,\tag{1}NEWLINE\]NEWLINE where \(u\) and \(v\) are the concentrations of the chemical materials \(U\) and \(V\), respectively; \(D_u\) and \(D_v\) are the diffusion coefficients, \(F\) is the in-flow rate of \(U\) from outside, \(F+k\) is the removal rate of \(V\) from reaction field.NEWLINENEWLINENEWLINEThe aim of this paper is to clarify the onset point of STC arising in (1) (the geometrical structure of the global bifurcation diagram of ordered states plays a key role in giving such a criterion) and to understand the mechanism which drives chaotic dynamics from a pattern formation point of view.