Stability of steady state and bifurcation in a high autocatalytic reaction diffusion system

A reactiondiffusion system based on the higher autocatalytic, within a closed region, is considered. The stability of the steady state (u,v)=(μ*,μ) is discussed first by the linearized theory. It is shown that a necessary condition for the bifurcation of this steady state to stable spatially non_uniform solutions is that the parameter D(n-1)2/(n-1) where D=λb/λa(λa,λb are the diffusion coefficients of chemical species A and B respectively). The nature of the spatially non_uniform solutions close to their bifurcation points is analyzed from a weakly nonlinear analysis.