Modelling And Analysis Of Integrated Pest Management Strategy

It is well-known that the theory of impulsive differential equation is not only richer than the corresponding theory of differential equation but also represent a more natural framework for mathematical modelling of many real world phenomena. In this thesis we establish some population dynamical models concerning integrated pest management (or IPM), mathematically I use the theory of semi-continuous dynamical system to globally investigate dynamical behaviors including the existence and stability of periodic solution. From the biological point of view, the mathematical results are full of biological meanings and can be used to provide reliable decision proof.In Chapter 2, a classical Lotka-Volterra predator-prey system is investigated, we analyze the dynamics of positive solutions of such model. In Chapter 3, the state-dependent impulsive system concerning inegrated pest management are proposed and investigated, that is, when the pest population reaching the economicinjury level, a comination of biological, cultural and chemical tacties that reduce pests to tolerable levels is used. Frist, we proved the exisence of order 1 periodic solution by using the properties of LambertW function and successor function. Secondly we also show that the order 1 periodic solution of the system is orbitally asymptotically stable under some condition by using the analogue of the Poincare criterion. Finally, we analyze a particular state-dependent impulsive system, we show that there exists an orbitally asymptotically stable order 2 periodic solution.