Rich dynamic of a stage-structured prey–predator model with cannibalism and periodic attacking rate

The dynamic behavior of a stage-structure prey–predator model with cannibalism for prey and periodic attacking rate for predator is investigated. Firstly, the permanence, locally and globally asymptotic stability analyses of the model with constant attacking rate are explored. After that, sufficient conditions for the permanence of the corresponding nonautonomous system with periodic attacking rate are obtained. Furthermore, numerical simulations are presented to illustrate the effects of periodic attacking rate. Simulation results show that the system with periodic attacking rate shows a rich behaviors, including period-doubling and period-having bifurcations, chaos and windows of periodicity.