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Diffusion-driven codimension-2 Turing-Hopf bifurcation in general Brusselator model
  • Lei Kong,
  • Changrong Zhu
Lei Kong
Guizhou University of Finance and Economics
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Changrong Zhu
Chongqing University
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Peer review status:UNDER REVIEW

05 May 2020Submitted to Mathematical Methods in the Applied Sciences
10 May 2020Assigned to Editor
10 May 2020Submission Checks Completed
12 May 2020Reviewer(s) Assigned


The spatiotemporal dynamics for general reaction-diffusion systems of Brusselator type under the homogeneous Neumann boundary condition is considered. It is shown that the reaction-diffusion system has a unique steady state solution. For some suitable ranges of the parameters, we prove that the steady state solution can be a codimension-2 Turing-Hopf point. To understand the spatiotemporal dynamics in the vicinity of the Turing-Hopf bifurcation point, we calculate and analyze the normal form on the center manifold by analytical methods. A wealth of complex spatiotemporal dynamics near the degenerate point are obtained. It is proved that the system undergoes a codimension-2 Turing-Hopf bifurcation. Moreover, several numerical simulations are carried out to illustrate the validity of our theoretical results.