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Diffusion-driven instability and bifurcation in the Lengyel-Epstein system. (English) Zbl 1146.35384
Summary: Lengyel-Epstein reaction-diffusion system of the CIMA reaction is considered. We derive the precise conditions on the parameters so that the spatial homogeneous equilibrium solution and the spatial homogeneous periodic solution become Turing unstable or diffusively unstable. We also perform a detailed Hopf bifurcation analysis to both the ODE and PDE models, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.
35K57Reaction-diffusion equations
35B10Periodic solutions of PDE
35K50Systems of parabolic equations, boundary value problems (MSC2000)
92B05General biology and biomathematics
35B32Bifurcation (PDE)