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Spatiotemporal pattern formation and multiple bifurcations in a diffusive bimolecular model. (English) Zbl 1203.35037
Summary: We have investigated a homogeneous reaction-diffusion bimolecular model with autocatalysis and saturation law subject to Neumann boundary conditions. We mainly consider Hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive equilibrium solution of the system. Our results suggest the existence of spatially non-homogeneous periodic orbits and non-constant positive steady state solutions, which implies the possibility of rich spatiotemporal patterns in this diffusive biomolecular system. Numerical examples are presented to support our theoretical analysis.
MSC:
35B36Pattern formation in solutions of PDE
35B32Bifurcation (PDE)
35K57Reaction-diffusion equations
35K51Second-order parabolic systems, initial bondary value problems
35K58Semilinear parabolic equations