
Meng Fan 
Northeast Normal University, School of Mathematics and Statistics 
11:00 am in MSB 318


This talk recalls our recent studies on the dynamics of nonautonomous predatorprey systems with environmental variations. First, the dynamics of a nonautonomous predatorprey system with BeddingtonDeAngelis functional response is wellstudied. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for periodic (almost periodic) case. Some interesting numerical simulations are presented to complement the analytical findings. Then, a predatorprey model of LotkaVolterra type with prey receiving timevariation of the environment is considered. Such a system is shown to have a unique interior equilibrium that is globally asymptotically stable if the timevariation is bounded and weakly integrally positive. In particular, the result tells that the equilibrium point can be stabilized even by nonnegative functions that make the limiting system structurally unstable. The method that is used to obtain the result is an analysis of asymptotic behavior of the solutions of an equivalent system to the predatorprey model. Finally, we discuss the persistence of equilibrium as periodic solution in a general framework. 