IMPACT OF FEAR AND HARVESTING EFFORT ON A DIFFERENTIAL-ALGEBRAIC PREY-PREDATOR MODEL BASED ON SQUARE ROOT FUNCTIONAL RESPONSE

An economic differential-algebraic prey-predator model incorporating square root functional response and fear of predators is presented in this current paper. The article is developing a prey-predator structure on the intention to an economic viewpoint through harvesting on prey species. The equilibrium points and stability status of both the differential-only model and differential-algebraic model are identified and examined. Impacts of fear effect on the stabilities of the model equilibrium points are studied. The Hopf bifurcation analysis is carried out concerning the prey species’ intensity of fear and growth rate. The singularity-induced bifurcation for zero and non-zero economic profits is discussed for the proposed system. A state feedback controller is constructed for zero economic profit to keep the persistence property of the prey-predator model. Numerical simulations and graphical presentations are provided in support of our analytical findings.