Dynamics Analysis Of A Predator-prey Model With Nonlinear Harvesting

Predator-prey model is a very important model in biological models.Harvest-ing rate is a very important factor in these kinds of models,excessive harvest may have a significant impact on the ecosystem,even destroy these kinds of species.The study of predator-prey model with harvesting rate of prey or predator or two species has a significant impact on the protection of ecological resources and economic de-velopment.A predator-prey model with Holling II response function harvesting has been studied.The conditions of the existence of positive constant equilibrium have been giv-en,applying the maximum principle of parabolic equations and Gronwall inequali-ties to give the upper bound of the positive solution.The local stability of the trivial equilibrium and the positive equilibrium is analyzed by the eigenvalue theory,the global stability of the trivial equilibrium and the positive equilibrium is proved by constructing Lyapunov function.A priori estimate of positive steady state solutions is obtained by applying the maximum and comparison principle,and nonexistence of non-constant steady state solutions is given by applying the Poincare inequali-ties.The existence of the positive equilibrium solution branch from the semi trivial solution is proven.