Hopf bifurcation in general Brusselator system with diffusion  

作　　者：郭改慧 吴建华 任小红 

机构地区：[1]College of Science,Shaanxi University of Science and Technology [2]College of Mathematics and Information Science,Shaanxi Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第9期1177-1186,共10页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10971124 and 11001160);the Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2011JQ1015 and 2009JQ100);the Doctor Start-up Research Fund of Shaanxi University of Science and Technology (No. BJ10-17)

摘　　要：The general Brusselator system is considered under homogeneous Neumann boundary conditions.The existence results of the Hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation （PDE） models are obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions are established.Moreover,some numerical simulations are shown to support the analytical results.At the same time,the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.The general Brusselator system is considered under homogeneous Neumann boundary conditions.The existence results of the Hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation （PDE） models are obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions are established.Moreover,some numerical simulations are shown to support the analytical results.At the same time,the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.

关 键 词：general Brusselator system Hopf bifurcation DIFFUSION stability 

分 类 号：O175[理学—数学]