Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative

This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications. Using bifurcation theory, bifurcations related to period doubling, Neimark–Sacker, and strong resonances are studied. Lastly, the analytical results are confirmed through numerical simulations using the MATLAB package MatContM, and a controller is applied to relieve the extreme instability within the system.