Dynamical Behaviors of a Fractional-Order Predator-Prey Model with Holling Type IV Functional Response and Its Discretization

摘要

In this paper, we investigate the dynamical behaviors of a fractional-order predator-prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark-Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.