Period-Doubling and Neimark-Sacker Bifurcations in a Discrete Fractional Predator-Prey Model with Harvesting

Abstract

This paper investigates a discrete-time fractional-order predator-prey model with proportional harvesting on the prey population. The model is derived using the piecewise constant argument method, allowing the incorporation of memory effects in a discrete framework. The existence and local stability of equilibria are analyzed via the Jacobian matrix and characteristic equation. Conditions for period-doubling and Neimark-Sacker bifurcations are established, revealing transitions to periodic and quasi-periodic dynamics. Numerical simulations illustrate the impact of harvesting intensity on system stability and oscillatory behavior. The results highlight the significant role of harvesting and memory in shaping predator-prey dynamics. Keywords: Population model; fractional derivative; harvesting; stability; bifurcation