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Hopf bifurcation in general Brusselator system with diffusion

  • Gai-hui Guo (郭改慧)Email author
  • Jian-hua Wu (吴建华)
  • Xiao-hong Ren (任小红)
Article

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.

Key words

general Brusselator system Hopf bifurcation diffusion stability 

Chinese Library Classification

O175.26 

2010 Mathematics Subject Classification

35K57 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gai-hui Guo (郭改慧)
    • 1
    Email author
  • Jian-hua Wu (吴建华)
    • 2
  • Xiao-hong Ren (任小红)
    • 1
  1. 1.College of ScienceShaanxi University of Science and TechnologyXi’anP. R. China
  2. 2.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anP. R. China

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