The Study Of Asymptotical Behaviors On Several Classes Of Nonautonomous Difference Competitive System

In this thesis, some theories and approaches related to discrete dynamics, functional analysis and numerical simulations are used to investigate dynamical behaviors such as the permanence, existence and global asymptotic stability of positive periodic solutions. The whole thesis is divided into four chapters.The first chapter introduces concisely the application background, the present development of relevant subjects about difference equations as well as the main work done in this thesis and some preliminaries.In the second chapter, we establish a corresponding nonautonomous difference form based on a two-species competitive differential system. By using the difference inequality skills and Brouwer fixed point theory, sufficient conditions which guaran- tee the permanence and the existence of positive periodic solutions are obtained, respectively. Moreover, we obtain the sufficient conditions for global asymptotic stability of positive periodic solutions. Biological interpretations and examples on the main results are also given.In the third chapter, based on the above difference system, we further consider the possible effect of more than one past generation on the density dependent popu- lation, and establish a nonautonomous difference competitive system with several discrete delays. By using the difference inequality skills, Mawhin continuous theory and Lyapunov function, sufficient conditions for the permanence, the existence and global asymptotic stability of positive periodic solutions of system are derived, respectively. Besides, biological interpretations and examples on the main results are given.In the fourth chapter, based on a distributed delay differential system of plankton allelopathy, we obtain a corresponding difference form with the help of a discretiza- tion technique and method. Then, by using the difference inequality skills, Mawhin continuous theory and Lyapunov function, sufficient conditions for the permanence, the existence and global asymptotic stability of positive periodic solutions of system are given, respectively. Besides, biological interpretations and examples on the main results are given.