Qualitative analysis of Holling IV predator-prey model with harvesting rates for preys and predators

This paper is devoted to the qualitative analysis of Holling IV predator-prey model with harvesting rates for preys and predators. Where the prey has the nonlinear density restriction and the predator has the linear density restriction. Discusses the properties of prey and predator's isoclines, obtain the sufficient and necessary condition of the existence of only positive equilibrium point. Furthermore, we study the boundedness of the system's solution and the properties of the equilibriums. By Dulac judging method, the condition of any cycles in the system and sufficient condition under which the only positive equilibrium point which is globally asymptotic stable is obtained. Finally the particular parameter system numerically simulated.