一类自催化反应系统的Hopf分歧与稳定性

Hopf Bifurcation and Stability for an Autocatalytic System

本文考虑一类带饱和项的自催化反应系统.我们首先讨论了常微分系统Hopf分歧的存在性,得到了渐近稳定的周期解.其次讨论了具有扩散项的偏微分系统,在扩散系数满足一定的条件下,得到了次临界的Hopf分歧的存在性,并且利用中心流形约化方法,判断出由该Hopf分歧产生的空间齐次的周期解是渐近稳定的.最后,借助Matlab软件形象地验证和刻画了文中的结论.

This paper concerns a chemical model with an autocatalysis and saturation law.First,the subcritical Hopf bifurcation is obtained for the ordinary differential system and the induced periodic solutions are locally asymptotically stable.Then the diffusive model is considered.When the diffusive coefficients satisfy certain conditions,the subcritical Hopf bifurcation is also obtained and the spatially homogeneous periodic solutions are asymptotically stable.At last,numerical examples simulated with Matlab are shown to support and strengthen the analytical conclusions.