Dynamics of a periodic switched predator–prey system with impulsive harvesting and hibernation of prey population

Abstract

Winter hibernation constitutes an effective strategy of animals in order to correspond survive cold environments and limited availability of food, it plays an important role in biological evolution. In this work, we firstly introduce hibernation behaviors of prey population into predator–prey systems with impulsive effect, then construct a periodic switched predator–prey system with winter hibernation in prey population and impulsive effect. We prove that the solutions of system (2.1) are uniformly ultimately bounded. We obtain the conditions of the globally asymptotically stable predator-extinction boundary periodic solution of system (2.1), and also obtain the permanent conditions of system (2.1). Finally, numerical analysis is employed to illustrate the results. Our results provide reliable tactic for the biological economics management and the protection of biodiversity.