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Zbl 1018.92033
Teng, Zhidong; Chen, Lansun
Permanence and extinction of periodic predator--prey systems in a patchy environment with delay. (English)
[J] Nonlinear Anal., Real World Appl. 4, No.2, 335-364 (2003). ISSN 1468-1218

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 2000:: *92D40 Ecology
34C60 Applications of qualitative theory of ODE
34K25 Asymptotic theory of functional-differential equations

Keywords: Lotka-Volterra system; dispersion; delay; predator-prey; permanence; extinction; periodic solution

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