Note on the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate

Abstract

Abstract We revisit the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate. By using the differential inequality theory and Bendixson–Dulac criterion, we show that if the system without cannibalism is permanent, then the system with cannibalism is also permanent. By developing some new analysis technique, we obtain a new set of sufficient conditions which ensure the global asymptotic stability of the nonnegative equilibrium, which means that, under some suitable assumption, prey cannibalism has no influence on the stability property of the predator free equilibrium. Our results essentially improve the corresponding results of Limin Zhang and Chaofeng Zhang.

Keywords

• Stage structure
• Predator–prey
• Cannibalism
• Permanence
• Global asymptotical stability