Mathematical Biology Seminar Abstract
Mar 11, 2015
Meng Fan
Northeast Normal University, School of Mathematics and Statistics
11:00 am in MSB 318

Dynamics of predator-prey systems with environmental variations

This talk recalls our recent studies on the dynamics of nonautonomous predator-prey systems with environmental variations. First, the dynamics of a nonautonomous predator-prey system with Beddington-DeAngelis functional response is well-studied. 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 predator-prey model of Lotka-Volterra type with prey receiving time-variation of the environment is considered. Such a system is shown to have a unique interior equilibrium that is globally asymptotically stable if the time-variation 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 predator-prey model. Finally, we discuss the persistence of equilibrium as periodic solution in a general framework.