The Study On Two Classes Of Nonautonomous Predator-Prey Systems With Delay And Impulsive Effects

In this paper, based on some theories related to discrete dynamics, continuousdynamics and impulsive differential dynamics, we make the methodical analysis onthe permanence and global attractivity of the positive solutions for proposed systemsand then present some examples and their corresponding numerical simulations. Thewhole paper is composed of three chapters:Chapter1reviews the research backgrounds and current study on the delayedpopulation dynamical system and impulsive population dynamical system, and brieflystates our main work done.In chapter2, we discuss the first model, which is based on the nonautonomouspredator-prey periodic system with continuously distributed delays, and derive acorresponding difference version. By using the difference inequality skills andconstructing a discrete Lyapunov function, sufficient conditions which guarantee thepermanence and global attractivity of the positive solutions are established. Also, anexample and its numerical simulations on the main results are also given.In chapter3, we discuss the second model, which is a predator-prey periodicdifferential system considering the effects of linear impulses and constant impulses.Sufficient conditions are derived for the permanence and global attractivity of thepositive solutions by using the theory of impulsive differential equation, analyticalskills and Lyapunov function. Moreover, we present an example and its numericalsimulations concerning our main results.