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Asymptotic behavior of a predator-prey system with diffusion and delays. (English) Zbl 0872.92019
Summary: The asymptotic behavior of solutions of a predator-prey system is determined. The model incorporates time delays due to gestation and assumes that the prey disperses between two patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier. Conditions are established for the permanence of the populations and the global attractivity of a positive equilibrium.
MSC:
92D40Ecology
34K25Asymptotic theory of functional-differential equations
34K99Functional-differential equations
34K20Stability theory of functional-differential equations