The Existence And Global Attractivity Of Positive Periodic Solution For Two Kinds Of Lotka-Volterra Systems

At present,the research of population dynamics model has achieved very good results.It has become the most popular topic in theoretical research of biological mathematics.The dynamic properties of the two subjects mainly include the boundedness of the solu-tion,the persistence of the population,the extinction,the global attraction,the existence of the periodic solution,etc.This paper mainly based on the extension theorem of the topological degree theory,the Liapunov functional,and the inequality estimation,and sys-tematically studies the two species of population with discrete time delay and feedback control.1.we give some results of the models,and then introduce several kinds of cooperative and competition models.Finally,we introduce some definitions and lemmas in this paper,as well as some research results and research models.2,we discuss the first model by means of continuation theorem,inequalities estimate methodand and Lyapunov functional method to established some sufficient conditions on the existence and global attractivity of positive periodic solution of the system.3,we discuss the second model by means of continuation theorem,inequalities esti-mate methodand and Lyapunov functional method to established some sufficient condi-tions on the existence and global attractivity of positive periodic solution of the system.4.the results obtained in this paper are discussed and summarized.