| 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. |