Dynamics of periodic switched systems describing a single population system with impulses and hibernation

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 construct periodic switched systems describing a single population system with impulsive input toxins in polluted environment. All solutions of system (2.1) are proved to be uniformly ultimately bounded. We prove that the population-extinction solution of system (2.1) is globally asymptotically stable. The permanent condition of system (2.1) is obtained. Finally, numerical analysis is inserted to illustrate the results. Our results provide reliable tactic basis for the practical biological economics management and the protection of biodiversity.