Fractional Prey-Predator Model: Stability, Refuge, 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.
Researchers have examined a fractional-order prey-predator model, incorporating prey refuge and fear effects within a Filippov system. The study confirms the model's mathematical consistency and ecological feasibility, proving the existence and uniqueness of solutions, as well as their non-negativity and boundedness. Analysis of equilibrium points indicates that the fractional order parameter influences stability, with lower orders leading to slower population convergence due to memory effects. Numerical simulations support these theoretical findings, highlighting how prey refuge can stabilize populations while the fear effect may destabilize them.
This research offers a more realistic mathematical framework for understanding complex ecological interactions and population dynamics in predator-prey systems.
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