Stability And Permanence Of Several Pest Control Impulsive Differential Models

Impulsive differential equation theory is an important branch of differential equation theory,which has been greatly developed in recent decades.From the perspective of mathematics,it transforms specific things in life into mathematical models.By studying the various dynamical properties of the mathematical model,the mathematical results can be applied to life,so as to achieve purposeful control over it.In this paper,several types of impulsive differential equation mathematical models are established for the comprehensive management of diseases and insect pests in agricultural production.We give some sufficient conditions of the local asymptotical stability,global attraction,and permanence for its impulsive differential model by using the comparison theorem of impulsive differential equations,Floquet multiplier theory,constructing Lyapunov functions,use also prove that the ecological mathematical model established in this paper will go to a dynamical ecological balance when period of using the impulse means of spraying chemical pesticides and releasing natural enemies to control pests is greater than a certain positive value.From the perspective of mathematics,the theoretical basis is given for comprehensive pest management to control the number of pests,which provides an important reference for agricultural production.This article mainly includes the following work:The first chapter introduces the research background of pest control and the concept of population dynamics.Chapter 2 introduces some mathematical propositions related to impulsive differential equations.Chapter 3 takes pests and natural enemies as targets,and establishes the pest-natural enemy Schoener impulse differential model to prove the boundedness of understanding,the local asymptotic stability of the periodic solution of pest extinction,and the continuous survivability of the system.Chapter 4 discusses the asymptotic stability of the periodic solutions of pest extinction under the action of viruses and the continued viability of the system.The above results are also proved from a mathematical point of view.The fifth chapter establishes an impulsive differential model for integrated pest management,and discusses the boundedness of general solutions,the local asymptotic stability and global attractivity of periodic solutions for pest extinction,and the permanence of the system,which is proved from a mathematical point of view.The correctness of the above results.The sixth chapter supplementally proves the permanence theorem of a five-dimensional integrated pest management impulse differential model.This result is a basis for studying the complexity and chaos of such systems.The results show that although the relationship between pests and crops is very complicated,they can coexist and be controlled under certain conditions.