一类高次自催化反应扩散系统平衡态的稳定性及分歧

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

研究了一类发生在密闭容器内且扩散系数不同的高次自催化反应,用线性化理论讨论了平衡态(u,v)=(μ ,μ)的稳定性,并且证明了由稳定态产生的分歧是稳定空间非一致解的必要条件是参数D(=λb/λa)<(n-1)2/(n-1)(其中λa,λb分别是化学物种A和B的扩散系数).进一步用弱非线性理论分析了接近分歧点的空间非一致解的性质.

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.