Dynamic Behaviors For Some Models Of Nonlinear Forest Insect Pests

Nowadays, the mathematical application in society economic and engineering technology becomes more and more popular. People use mathematical models to reveal the internal mechanism of the system and make predictions.In this paper, the system of forest insect pests is studied through mathematical models . Three population dynamical models: continuous , impulsive and delayed are established respectively. Dynamical properties including stability,permanence,controllability of these models are subsequently studied.In chapter two, the nonlinear models for two kinds of forest insect pests are described by ordinary differential equations. Firstly, the critical threshold of the system is given, the existence and uniqueness of equilibrium point is proved. Secondly, the dynamical property for two models are studied by the Hurwitz criterion and Lyapunov stability theory. Thirdly, the nonexistence of limit cycles is proved by the Bendixson-Dulac discriminance with an appropriate choice of the Dulac function, hence the insect pests would be controlled. Finally, the conclusion of the theory is testified by numerical simulation.In chapter three , a three-population food chain model which concerning about impulsive releasing predators (natural enemies) at fixed moment is proposed based on the integrated pest management program. The Floquet theory and the comparison theorem of impulsive differential equation are used to study the existence and global asymptotic stability of pest-eradication periodic solution. The continuous existence of the system are obtained.In chapter four, with Bursaphelenchus Xylophilus as an instance, the time delay discrete interconnected system model consisiting of Monochamus alternatus, Bursaphelenchus Xylophilus and pine trees subsystems is introduced. The interconnected guaranteed cost control model is presented. By means of Lyapunov-Krasovskii stability theory and linear matrix inequalities , sufficient conditions for uniformly asymptotic stabilization of the system are obtained. The controllability of the system and the stabilized control law of the system is given.