一类高次自催化耦合反应扩散系统的分歧和斑图

Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System

考虑了一类由于自催化剂的耦合而发生的反应扩散系统的空间结构.利用线性化理论讨论了平衡态解的稳定性并且证明了在非耦合系统中空间非一致解出现分歧的必要条件.进一步,利用弱非线性理论讨论了分歧点并且给出了弱耦合系统的图灵分歧解的振幅方程及其性质.

Spatotemporal structures arising in two identeal cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst, are discussed. The stability of the unique homogeneous steady state is obtained by the linearized theory. A necessary conditon for bifurcations to spatially non-uniform solutions in uncoupled and coupled systems is given. Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory. Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system.