Dynamic behaviors of a periodic Lotka-Volterra commensal symbiosis model with impulsive

Abstract

In this paper, the dynamic behaviors of an impulsive periodic Lotka-Volterra commensal symbiosis model is studied in this paper. Firstly, by constructing a suitable Lyapunov function and using the comparison theorem of impulsive differential equation, some sufficient conditions which ensure the permanence and global attractivity of the system are obtained; Secondly, conditions which guarantee that one species in the system are permanent while the remaining species is driven to extinction is obtained. Thirdly, conditions which ensure the extinction of the system are also obtained. Our results show that, for Lotka-Volterra commensal symbiosis model, impulsive is one of the important reasons that can change the long time behaviors of species.