GUO Gai-hui, WU Jian-hua, REN Xiao-hong, YU Peng. Hopf Bifurcation in the General Brusselator System With Diffusion[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009
Citation: GUO Gai-hui, WU Jian-hua, REN Xiao-hong, YU Peng. Hopf Bifurcation in the General Brusselator System With Diffusion[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009

Hopf Bifurcation in the General Brusselator System With Diffusion

doi: 10.3879/j.issn.1000-0887.2011.09.009
  • Received Date: 2010-11-04
  • Rev Recd Date: 2011-06-08
  • Publish Date: 2011-09-15
  • The general Brusselator system was considered under homogeneous Neumann boundary conditions.The existence results of Hopf bifurcation to the ODE and PDE models were obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions were also established.Moreover,some numerical simulations were shown to support the analytical results.At the same time,the figures of positive steady-state solutions and spatially inhomogeneous periodic solutions were drawn,which supplement the analytical results.
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