Permanence and extinction of periodic predator-prey systems in a patchy environment with delay

Authors:
Zhidong Teng;Lansun Chen
Affiliations:
Department of Mathematics, Xinjiang University, Urumqi 830046, People's Republic of China;Institute of Mathematics, Chinese Science Academia, Beijing 100080, People's Republic of China
Venue:
Nonlinear Analysis: Real World Applications
Year:
2003

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Abstract

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 the 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.