Two Classes Of Integrated Pest Management Predator-prey Model With Allee Effect

As a country with vast expand of territory,China possesses relatively abundant agricul-tural resources.However,in recent years the biological insect pest outbreaks frequently.Al-though pests harm crops,only when their number reaches a certain amount,they can causes economic losses to human beings.Therefore,it is necessary to take practical prevention and control measures to prevent their spread when the number of pests reaches certain threshold level.In this context,the paper introduces two pest control strategies:releasing the predator and spraying pesticide,and proposes two classes of predator-prey model with impulsive state feedback control and Allee effect to study the dynamical behavior of the interaction between pests and their natural enemies.In Chapter 2,we consider a class of Leslie-Gower predator-prey model with state feed-back impulsive control and Allee effect on the predator,where the yield of the predator released and intensity of pesticide sprayed are linearly dependent on the pest control level.The positivity and boundedness of the solution of the uncontrolled system are given,and the sufficient conditions for the global asymptotically stability of the positive equilibria are ob-tained.Then the existence of the order-1 periodic solution of the control system is discussed by means of the successor function method,and the condition for the stability of the order-1 periodic solution is presented.Besides,in order to determine the optimal quantity of natural enemies released and the optimal intensity of pesticide sprayed,we construct and analyze an optimization model with the aim of minimizing input cost.The results show that,based on the control strategies proposed in this paper,the number of pests can be limited to an economic threshold and displays periodic variation.In Chapter 3,we establish and analyze a class of Lotka-Volterra predator-prey model with integrated pest management and Allee effect.We mainly discuss the case that the system has two positive equilibrium.One of the positive equilibrium is a saddle point.If the another one is a stable focus(or node)point and there is no limit cycle for the continuous system,we can verify the existence and stability of the order-1 periodic solution of the control system by applying the successor function method and the analogy of Poincar6 criterion.If the another equilibria is an unstable focus(or node)point and the continuous system has a stable limit cycle,we prove that the control system has at last four kinds of order-1 periodic solutions within the limit cycle.And these theoretical results are verified by numerical simulations.