The Study Of Almost Periodic Solution For Biological Models With Impulsive Or Feedback Controls

This thesis mainly studies the several kinds of biological model with impulses or feedback controls. By means of different research methods, the sufficient condi-tions on the existence of almost periodic solutions of the several kinds of systems have been obtained. It is consists of four chapters.In Chapter 1, introduce issues arising from the historical background and main tasks of this article.In Chapter 2, discuss the existence of almost periodic solution in a model of hematopoiesis with impulsive. Our approach is based on the estimation of the Cauchy matrix of the corresponding linear impulsive differential equations. We employ the contraction mapping principle and the Gronwall-Bellman inequality to obtain the existence and stability of the almost periodic solution of the system. Our results extend some known results.In Chapter 3, discuss permanence and global attractivity of positive almost periodic solutions for impulsive n-specise Lotka-Volterra systems. By construct-ing a suitable Lyapunov function and using some analysis techniques, we obtain some sufficient conditions which guarantee existence of a unique positive almost periodic solution of the system. By using impulsive inequalities, we obtain permanent of the system.In Chapter 4, discuss the almost periodic solution of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and feed-back controls. We construct a suitable Lyapunov function and use some analysis techniques to obtain existence and asymptotic stability of almost periodic solution of the system. By applying differential inequalities, we obtain permanent of the system.