Bifurcation Patterns in a Discrete Predator–Prey Model Incorporating Ratio-Dependent Functional Response and Prey Harvesting

Abstract

This work examines a discrete Leslie-Gower model of prey-predator dynamics with Holling type-IV functional response and harvesting effects. The study includes the existence and local stability analysis of all fixed points. Using center manifold theory, the codimension-1 bifurcations, viz. transcritical, Neimark–Sacker, fold, and period-doubling bifurcations, are determined for varying parameters. Moreover, the existence of codimension-2 Bogdanov–Takens bifurcation and Chenciner bifurcation is demonstrated, requiring two parameters to vary for the bifurcation to occur, and the non-degeneracy conditions for Bogdanov–Takens bifurcation are determined. An extensive numerical study is conducted to confirm the analytical findings. A wide range of dense, chaotic windows can be seen in the system, including period-2, 4, 8, and 16, period-doubling bifurcations, Neimark–Sacker bifurcations, and Chenciner and BT curves following two-parameters bifurcations. Further, it is also shown that the effect of harvesting parameter of the model for which the population dies out.