Volume 6, Number 3, Fall 1998
PERSISTENCE AND PERIODIC ORBITS FOR
TWO-SPECIES PREDATOR-PREY SYSTEM
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.