Abstract
In this paper, spatiotemporal dynamics for a general reaction–diffusion system of Brusselator type under the homogeneous Neumann boundary condition is considered. It is shownthat the reaction–diffusion system has a unique steady state solution. For some suitable 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
