Permanence of predator-prey system with infinite delay

Abstract

In this paper we consider a predator-prey system with periodic coefficients and infinite delay, in which the prey has a history that takes them through two stages, immature and mature. We provide a sufficient and necessary condition to guarantee the permanence of the system. The system has a positive periodic solution under this condition. Some known results are extended to the delay case.

Keywords

• Predator-prey system
• stage structure
• permanence
• periodic solution
• infinite delay.