Dynamics of a Discrete-Time Predator–Prey System with Holling II Functional Response

The dynamics behavior of a discrete-time predator–prey system, with Holling II functional response, is analyzed. The model shows a rich dynamical behavior in the feasible region. Some invariant sets are found and parameter conditions for the existence and stability of the fixed points are given. A parameter region where the system exhibits either a period-doubling or a Neimark–Sacker bifurcation is shown. In addition, conditions are provided on parameters that lead to chaotic dynamics. Finally, to illustrate our theoretical analysis some numerical simulations are shown.