Diffusion-driven instability and Hopf bifurcation in Brusselator system  

作　　者：李波 王明新 

机构地区：[1]Department of Mathematics,Southeast University,Nanjing 210018,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第6期825-832,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10771032);the Natural Science Foundation of Jiangsu Province (BK2006088)

摘　　要：The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.

关 键 词：Brusselator system Hopf bifurcation stability diffusion-driven Hopf bifurcation 

分 类 号：O175.29[理学—数学]