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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (9): 1177-1186.doi: https://doi.org/10.1007/s10483-011-1491-6

• Articles • 上一篇    下一篇

Hopf bifurcation in general Brusselator system with diffusion

郭改慧1 吴建华2 任小红1   

  1. 1. College of Science, Shaanxi University of Science and Technology, Xi’an 710021, P. R. China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P. R. China
  • 收稿日期:2010-11-04 修回日期:2011-06-08 出版日期:2011-09-02 发布日期:2011-09-02

Hopf bifurcation in general Brusselator system with diffusion

GUO Gai-Hui1, WU Jian-Hua2, REN Xiao-Hong1   

  1. 1. College of Science, Shaanxi University of Science and Technology, Xi’an 710021, P. R. China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P. R. China
  • Received:2010-11-04 Revised:2011-06-08 Online:2011-09-02 Published:2011-09-02

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773

被引次数

7

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.

Abstract: 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.

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