一类反应扩散系统的分歧与斑图

本文研究了一类发生在密闭容器中的不可激活的高次自催化反应扩散系统．在适当的条件下,用渐进近似的方法讨论了系统平衡态的稳定范围;用多重尺度的方法证明了当扩散系数λ充分小时,系统出现两种类型的斑图,一类是由Hopf分歧引出的驻波斑图;另一类是由 Pitchfork分歧引出的定波斑图．进一步还讨论了,在分歧点附近,对于大于空间或等于空间波数的小扰动,斑图是局部稳定的,而小于自身空间波数的小扰动,斑图是不稳定的．

Pattern and Bifurcation Formation in a Reaction Diffusion System

In this paper a reaction diffusion system based on the higher autocatalator, with the reaction taking place inside a closed vessel, is considered. Under suitable conditions, we examine the local stability of the steady state via asymptotic approximations and show that only when the diffusion coefficient A is sufficient small, two types of patterns occur, standing-wave patterns arising out of Hopf bifurcation, together with steady-wave patterns arising out of Pitchfork bifurcation, each pattern is shown to be partially stable to small disturbances composed of its own, or any higher spatial wave numbers. However, the pattern is unstable to disturbances with smaller spatial wave number than its own.