Strong resonance bifurcations and intricate behavior on a discrete prey–predator model with complex network: Immigration on prey and harvesting on predator

This paper investigates a discrete predator–prey model that incorporates immigration on prey population and predator is experienced with harvesting. We identify the model’s fixed points and analyze their stability. Since the harvesting of prey and the rate at which prey converted into predators are ecologically significant, their impact has been examined by selecting them as bifurcation parameters. Analytically, we demonstrate that the discrete model can exhibit a series of codimension-1 bifurcations, specifically Neimark–Sacker (NS) and period-doubling (PD) bifurcations, as well as codimension-2 resonance bifurcations (1:2, 1:3, and 1:4) at a unique fixed point, obviously positive, which are fundamental phenomena in discrete dynamical systems. The stability of these bifurcations is analyzed using the critical normal form theory. We explore the model’s dynamic behavior in response to changes in control parameters. We quantitatively simulate the graphical depiction of bifurcation, maximal Lyapunov exponents, fractal dimensions, and phase diagrams, presented to validate the analytical findings and illustrate the model’s complex and intricate dynamics. It is observed that parameter values have a considerable effect on the behavioral dynamics of the proposed model. Additionally, the OGY chaos control technique is applied to eliminate the inherent chaos in the model. Also, Bifurcations are investigated in a coupled network discrete predator–prey model. Numerical simulations demonstrate that chaotic behavior emerges in complex dynamical networks when the coupling strength parameter reaches its critical value. All theoretical findings related to stability, bifurcation, and chaotic transitions in the coupled network are supported by numerical simulations.