Applied Mathematics and Mechanics

, Volume 29, Issue 6, pp 825–832 | Cite as

Diffusion-driven instability and Hopf bifurcation in Brusselator system

  • Bo Li (李波)Email author
  • Ming-xin Wang (王明新)


The Hopf bifurcation 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.

Key words

Brusselator system Hopf bifurcation stability diffusion-driven Hopf bifurcation 

Chinese Library Classification


2000 Mathematics Subject Classification

35J55 92D25 


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Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingP. R. China
  2. 2.School of Mathematical ScienceXuzhou Normal UniversityXuzhouP. R. China

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