The influence of non-linear harvesting on a web of two prey with one predator, combined with fear and refuge strategies concerning prey populations

Abstract

Under the influence of various functional responses: Beddington–DeAngelis and Holling type IV  via predator interaction with two different kinds of prey populations in a web containing all these creatures, tends for discussing two distinct types of investigations, analytical and numerical,  the proposed model joining two defense strategies concerning the prey populations, fear effects and refuge respectively, with presentence of the force of nonlinear harvesting act as a pressure on both prey populations,  the system’s positivity and boundedness is the analytical already start with, seven acceptable equilibrium points find the existence, then the Jacobian and Lyapunov methods concerning these equilibria utilize to understand local and global stability conditions. Confirming analytical investigations via numerical analysis simulations, where the analytical results assert that fear and refuge stabilize population dynamics and reinforce coexistence. Still, while acting, the nonlinear harvesting can play a crucial role in determining the system's coexistence, extinction, or biodiversity loss. Sustaining predator–prey ecosystems confirms the Importance of Indirect strategies, as fear and refuge, and harvesting.