The Study Of A Nonautonomous Delay Single Species Difference System With Feedback Control

In this thesis, some theories and approaches related to difference equation, functional analysis and numerical simulations are used to investigate dynamical behaviors including the permanence, existence and global asymptotic stability of positive periodic solutions for a nonautonomous delay single species difference system with feedback control. The whole thesis is divided into four chapters.The first chapter introduces the development history about biological mathematics and population ecology, the biological background of feedback control and its present development as well as the main work done in this thesis.The second chapter introduces concisely some preliminary knowledge which relevant to this thesis, including definition, lemma and symbolic description which used throughout the thesis.In the third chapter, we introduce feedback control and delays into an autonomous single species differential system, and establish a corresponding nonautonomous delay difference system with feedback control. Firstly, by using the analysis technique and difference inequalities, we investigate the permanence of the system; secondly, we consider the existence and global asymptotic stability of positive periodic solutions by using Mawhin continuous theory and Lyapunov discrete function; thirdly, we give two specific examples and their corresponding numerical simulations; finally, discussion and biological interpretations on the main results are given.In the fourth chapter, we put forward some possible researches which can do in the future.