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Multiple bifurcations and spatiotemporal patterns for a coupled two-cell Brusselator model. (English) Zbl 1254.35115
Summary: A coupled two-cell Brusselator model with diffusion effect subject to Neumann boundary condition is considered. Hopf bifurcations and global steady state bifurcations which bifurcate from the unique positive constant equilibrium point are investigated in detail. Meanwhile, Turing instability occurs when diffusion is present. Particularly, we show the existence of spatially inhomogeneous periodic solutions and non-constant steady state solutions, which exhibit rich spatiotemporal patterns in this coupled Brusselator system. Some numerical simulations are presented to illustrate the theoretical results obtained.
MSC:
35K51Second-order parabolic systems, initial bondary value problems
35B10Periodic solutions of PDE
35B32Bifurcation (PDE)