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Volume 6,     Number 3,     Fall 1998

 

PERSISTENCE AND PERIODIC ORBITS FOR
TWO-SPECIES PREDATOR-PREY SYSTEM
WITH DIFFUSION
XINYU SONG AND LANSUN CHEN

Abstract. In this paper we consider the predator-prey system in which prey species can diffuse between two patches, while the predator species is confined to one patch and cannot diffuse. It is proved that the system can be made persistent. Further, if the system is a periodic system, it can have a strictly positive periodic orbit which is globally asymptotically stable under the appropriate conditions.

 

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