Qualitative analysis of a discrete conformable fractional predator-prey model with effort-based harvesting

This paper explores the complex evolutionary dynamics of a discrete-time predator-prey model formulated using conformable fractional derivatives with effort-based harvesting as a crucial socio-economic factor. By employing the piecewise-constant approximation method, we bridge the gap between continuous biological interactions and discrete-time modeling. We establish the existence and local stability of fixed points. A key contribution of this work is the analytical derivation of sufficient conditions for Neimark–Sacker and flip bifurcations, which show how fractional orders and harvesting affect the transitions from stability to periodic and chaotic regimes. To restrain chaotic behavior and restore the system to a stable state, a hybrid control strategy is applied. Numerical simulations are provided to validate our results, demonstrating that the conformable fractional-order approach offers a more comprehensive and flexible framework for studying population dynamics.