Bifurcation, chaos analysis and control in a discrete-time predator–prey system

The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory. The existence and stability of fixed points for the model are discussed. It is showed that under certain conditions, the system undergoes a Neimark–Sacker bifurcation when bifurcation parameter passes a critical value, and a closed invariant curve arises from a fixed point. Chaos in the sense of Marotto is also verified by both analytical and numerical methods. Furthermore, to delay or eliminate the bifurcation and chaos phenomena that exist objectively in this system, two control strategies are designed, respectively. Numerical simulations are presented not only to validate analytical results but also to show the complicated dynamical behavior.