A discrete-time predator–prey model is investigated in this paper. In considered model, the population is assumed to follow the model suggested by Ricker 1954. Existence and stability of equilibria are studied. Numerical simulations reveal that, depending on the parameters, the system has complicated and rich dynamics and can exhibit complex patterns. Also the bifurcation diagrams are presented.

The dynamical behavior of a discrete predator-prey system with a nonmonotonic functional response is investigated in this work. We study the local asymptotic stability of the positive equilibrium of the system by examining the characteristic equation of the linearized system corresponding to the model.By choosing the growth rate as a bifurcation parameter, the existence of Neimark-Sacker and period-doubling bifurcations at the positive equilibrium is established. Furthermore, the effects of perturbations on the system dynamics are investigated. Finally, examples are presented to illustrate our main results.

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