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Permanence and extinction of periodic predator–prey systems in a patchy environment with delay. (English) Zbl 1018.92033
Summary: This paper studies two species predator-prey Lotka-Volterra type dispersal systems with periodic coefficients and infinite delays, in which the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. Sufficient and necessary conditions of integrable form for permanence, extinction and the existence of positive periodic solutions are established, respectively. Some well-known results on the nondelayed periodic predator-prey Lotka-Volterra type dispersal systems are improved and extended to the delayed case.
MSC:
92D40Ecology
34C60Qualitative investigation and simulation of models (ODE)
34K25Asymptotic theory of functional-differential equations