具有扩散的Brusselator系统的Hopf分支(英文)  

Hopf Bifurcationin the Brusselator System with Diffusion

作　　者：郭改慧[1] 李兵方[2] 

机构地区：[1]陕西科技大学理学院,陕西西安710021 [2]陕西铁路工程职业技术学院,陕西渭南714000

出　　处：《应用数学》2011年第3期467-473,共7页Mathematica Applicata

基　　金：Supported by NSFC(10971124,11001160);the National Science Foundation for Postdoctoral Scientists of China(20090461281);the DrStart-up Scientific Research Foundation of SUST(BJ10-17);the Natural Science Basic Research Planin Shaanxi Province of China(2011JQ1015)

摘　　要：在齐次Neumann边界条件下,研究了Brusselator系统的Hopf分支问题.证明了当参数满足一定条件时,Brusselator常微分系统的平衡解和周期解是渐近稳定的,而相应的偏微分系统的空间齐次平衡解是不稳定的;如果适当选取参数,那么Brusselator偏微分系统出现Hopf分支.同时,利用中心流形定理证明了Hopf分支解的稳定性.最后给出一些数值模拟的例子以验证和补充理论分析结果.The Brusselator system subject to homogeneous Neumann boundary conditions is investigated. It is firstly shown that the homogeneous equilibrium solution becomes turing unstable or diffusively unstable when parameters are chosen properly. Then the existence of Hopf bifurcation to the ODE and PDE models is obtained. Examples of numerical simulations are also shown to support and supplement the analytical results.

关 键 词：Brusselator系统 HOPF分支 扩散 稳定性 

分 类 号：O175[理学—数学]