Stability and Hopf bifurcation analysis of a fractional-order Filippov prey-predator model with prey refuge and fear effects

This study investigates the stability of a fractional-order Filippov prey-predator model that incorporates the ecological complexities of prey refuge and the fear effect. The primary research question is: How do fractional-order dynamics, combined with non-smooth Filippov switching mechanisms, influence the long-term stability and persistence of predator-prey populations? We establish the existence and uniqueness of the solution, ensuring the model’s mathematical consistency. Key results include the proof of solution non-negativity and boundedness, confirming ecological feasibility, and a detailed local and global stability analysis of equilibrium points. Our analysis reveals that the fractional order parameter θ significantly modifies stability conditions, with lower orders inducing slower convergence and prolonged transients, reflecting memory effects. Numerical simulations corroborate the theoretical findings and illustrate the stabilizing impact of prey refuge and the destabilizing potential of the fear effect. This work demonstrates that a fractional-order Filippov framework provides a more nuanced and realistic representation of ecological dynamics than its integer-order counterpart.