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Asymptotic periodicity of a food-limited diffusive population model with time-delay. (English) Zbl 1096.35123
The authors discuss the stability and the asymptotic behavior of solutions for some reaction diffusion food-limited population model with delay. First, the authors establish sufficient conditions for the global asymptotic stability of the equilibrium zero with respect to nonnegative solutions. Second, the authors establish the existence of a unique periodic solution which is globally attractive. The authors discuss also the effect of the delay on the asymptotic behavior of solution. For illustration, several examples with numerical simulations are provided.

MSC:
35R10 Partial functional-differential equations
92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
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