Dynamics of a Fractional Order Harvested Predator-Prey Model Incorporating Fear Effect and Refuge

Abstract

This study presents a fractional-order predator-prey dynamics model that considers the impact of fear, refuge, and harvesting on the population, respectively. The proposed model uses the Caputo fractional derivative to successfully obtain the memory effects of this interaction between predators and preys. We prove the existence and uniqueness of solution to ensure the non-negativity and boundedness of the system, which is indispensable for maintaining biologically feasible populations. The stability analysis is conducted on the equilibrium points at local and global levels, explaining the conditions that guarantee these points are stable or lead to periodic dynamics through Hopf bifurcation. To support the analytical results, numerical simulations are provided, which demonstrate the essential roles played by fear, refuge, and harvesting in the survival of prey and the overall dynamics of the system.