Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population

This study examines the discrete prey-predator model in the sense of Caputo fractional derivative by incorporating harvesting on the predator population and immigration on the prey population. We establish the topological categories of the model’s fixed points. We show analytically that a fractional order prey-predator model supports both a Neimark–Sacker (NS) bifurcation and a period-doubling (PD) bifurcation under specific parametric circumstances. Using the central manifold and bifurcation theory, we provide evidence for NS and PD bifurcations. It has been discovered that the parameter values and the initial conditions have a significant influence on the dynamical behavior of the fractional order prey-predator model. Furthermore, two chaos management strategies are applied to eliminate the chaos that objectively exists in the model. Finally, numerical simulations are used to demonstrate complicated and chaotic behavior in order to support our theoretical and analytical discussions.