Dynamic Analysis Of Integrated Pest Management And Its Optimal Control Strategy

Agriculture is the foundation of economic development,social stability and national independence.Pest damage is one of the important factors that restrict the sustainable and stable development of agricultural production.Pest damage has become an important bottleneck restricting agricultural development and an important limiting factor that directly affects agriculture,rural development and the income growth of farmers.Therefore,three integrated pest management models are established and studied in this paper.Firstly,a predator-prey model with Allee effect and ratio-dependent is constructed.Secondly,we establish a Cydia Pomonella integrated management predator-prey model with Smith growth and linear feedback control.Finally,an integrated pest management model with ratio-dependent and impulsive feedback control is investigated,the dynamic properties of the model are discussed by using Poincare mapping.This paper has the following five chapters.Chapter 1,this chapter introduces impulsive differential equations and methods for controlling pests,and gives some concepts and lemmas.Chapter 2,a predator-prey model with Allee effect and ratio-dependent is constructed,and the impulse parameter linearity is dependent on controlling level.Firstly,the existence condition of the homoclinic cycle is obtained by analyzing the control parameter q.The existence,uniqueness and asymptotic stability of the periodic orbit are discussed by using the geometric theory of the differential equations,the method of successor functions and analog of the Poincare criterion.Secondly,we formulate a control optimization with a minimal total cost in pest management and obtain an optimal economic threshold.Finally,we verify the correctness of theoretical results by numerical simulation.Chapter 3,Cydia Pomonella has great influence on the output and quality of apple.Therefore,it is an interesting subject to find out the optimum control strategy of Cydia Pomonella.A Cydia Pomonella integrated management predator-prey model with Smith growth and linear feedback control is established in this chapter.Firstly,we prove the existence and uniqueness of order one periodic solution by using differential equation geometry theory and successor function method.Secondly,the stability of order one periodic solution is proved by using the geometric method.Finally,with the discussion of different parameters,we verify the correctness of theoretical results by numerical simulations,and demonstrate the advantages and disadvantages of biological control strategy,chemical control strategy and integrated control strategy.Moreover,the optimization model with minimum cost is established by using order one periodic solution and optimal control level of the model is obtained.Chapter 4,an integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this chapter.Firstly,we determine the Poincare map which is defined on the phase set and discuss its main properties including monotonicity,continuity,discontinuity.Secondly,the existence and stability of boundary order one periodic solution is proved by the method of Poincare map.According to the Poincare map and related differential equation theory,the conditions of the existence and global stability of the order one periodic solution are obtained when Φ(yA)≤ yA,and we prove the sufficient and necessary conditions for the global asymptotic stability of order one periodic solution when Φ(yA)>yA.Furthermore,we prove the existence of order-k(k≥2)periodic solution under certain conditions.Finally,we verify the correctness of main results by numerical simulation.Chapter 5,we summarize the results of this article and make a prospect of future research directions.