The Study For Two Classes Of Population Systems With Variable Harvesting Rate And Impulsive Effects

By applying some theories related to continuous dynamics, discrete dynamicsand impulsive dynamics, and some approaches from nonlinear analysis and numericalsimulation, the asymptotic behaviors for a class of two-species predator-prey systemwith variable harvesting rate and a class of two-species competitive system withmixed impulses effect are studied respectively in this thesis. These studies includepersistence, existence and global asymptotic stability of positive periodic solution forthe predator-prey system, and persistence, competitive exclusion principle (partialextinction) and globally attractivity of the positive solutions for the competitivesystem. The whole thesis is divided into three chapters.The first chapter concisely introduces the research history and present situationof the population ecology as well as the main work done in this thesis and somepreliminary knowledge.In the second chapter, we introduce an S-shaped variable harvesting rate intoprey species on the basis of a two-species predator-prey periodic differential systems,and establish a corresponding nonautonomous difference system by usingdiscretization skills. Then applying difference inequality and Brouwer fixed pointtheory, sufficient conditions of persistence, existence and global asymptotic stabilityof positive periodic solution for the system are derived respectively. Some examplesand numerical simulation on the main results are also given.In the third chapter, we consider the mixed effects of constant impulses andlinear impulses on a two-species competitive periodic differential system, andestablish a corresponding impulsive differential system. Then applying impulsivedifferential integral inequalities, impulsive differential equation comparison theoremand Lyapunov function method, sufficient conditions of persistence, competitiveexclusion principle (partial extinction) and globally attractivity of the positivesolutions for the system are derived respectively. Some examples and numericalsimulation on the main results are also given.