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Bifurcations of spatially nonhomogeneous periodic solutions and steady state solutions are rigorously proved for a reaction-diffusion system modeling CIMA chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics including Turing instability and oscillatory behavior. Examples of numerical simulation are(More)
a r t i c l e i n f o a b s t r a c t Keywords: Diffusive predator–prey system Holling type-II functional response Hopf bifurcation Steady state bifurcation Spatially non-homogeneous periodic orbits Global bifurcation A diffusive predator–prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf(More)
The Lengyel–Epstein reaction–diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that the constant equilibrium solution is globally asymptotically stable when the feeding rate of iodide is small. We also show that for small spatial domains, all solutions eventually converge to a spatially homogeneous and(More)
Bifurcations of spatially nonhomogeneous periodic solutions and steady state solutions are rigorously proved for a reaction-diffusion system modeling CIMA chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics including Turing instability and oscillatory behavior. Examples of numerical simulation are(More)
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