布鲁塞尔子的柱对称定态结构(二)——定态解的计算和分析

Column Symmetric State Structures of Brusselator Model( Ⅱ) ——The Calculation and Analysis of the Steady State Solution

本文在布鲁塞尔子的柱对称定态解构造的基础上,从布鲁塞尔子的反应扩散方程出发,利用稳定性分析和分支点理论详细地计算了布鲁塞尔子的柱对称定态解.计算结果表明,布鲁塞尔子的空间耗散结构呈柱对称,不仅随r变化,还受到z的调制;当第一分支点对应的参数kn'=k1,m'=1时,在柱的中心出现一个高浓度区.该研究结果对于了解演化着的生物化学和生命体系中的柱型结构具有一定的指导意义.

On the basis of the construction of the steady state solution, we calculated the column symmetric state structures of Brusselator Model by using the bifurcation theory from the reaction-diffusion equation of the Brusselator. The results show that its spatial dissipative structure presents the column symmetric ordered structure and changes with r andz, if the parameters of the first branch point correspond to k n＇ = k1 , m＇ = 1, there will be a high concentrative range in the centre of the column. The conclusions provide a useful reference for the evolution of the practical systems, especially the column-type structures of biological systems.