Stability Analysis Of Two Classes Of Delayed Pest Management Model With Stage Structure

Predator-prey models are studied by many authors.In this paper we mainly study the stability of two kinds of pest management models with stage structure and time delay.First,a syrphid fly-aphid model with stage structure and time delay for the predator is investigated.We discuss the positive and boundedness of the solution of the system.By calculating the corresponding characteristic equation we discuss the local stability of the equilibria and the existence of Hopf bifurcation.By using the persistence theory on infinite dimensional systems,it is proven that the system is permanent if the coexistence equilibrium exists.By constructing Lyapunov function and using Lasalle invariant principle and the comparison theorem,the global stability of the equilibria are also discussed.Numerical simulations are carried out to illustrate the main results.Next,based on the biological control strategy,a pest management model with time delay and stage structure for the pest is investigated,by releasing regularly the natural to control the pests.Using the theories and methods of impulsive and delayed differential equations,sufficient conditions are obtained,which guarantee the global attractivity of pest-eradication periodic solution and permanence of the system.Numerical simulations are carried out to illustrate the main results.