Permanence, extinction and periodic solution of predator–prey system with Beddington–DeAngelis functional response

In this paper we study permanence, extinction and periodic solution of periodic predator–prey system with Beddington–DeAngelis functional response. We provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent. In addition, sufficient condition is derived for the existence of positive periodic solution. This paper improves some main results obtained by Fan and Kuang [M. Fan, Y. Kuang, Dynamics of nonautonomous predator–prey system with the Beddington–DeAngelis functional response, J. Math. Anal. Appl. 295 (2004) 15–39].