Almost Periodic Solutions Problems For Several Kinds Of Biological Models

This thesis mainly studies almost periodic solutions problem for several kinds of biological models. 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, we introduce issues arising from the historical background and main tasks of this article.In Chapter 2, we discuss the existence and uniqueness of almost periodic solution of Volterra competition system with feedback controls. By applying dif-ferential inequalities, we obtain permanent of the system. We construct a suitable Lyapunov function and use some analysis techniques to obtain existence and u-niqueness of almost periodic solution of the system.In Chapter 3, the n-dimensional model of competition instead the original two-dimensional competition model, we discuss the existence of almost periodic solution for impulsive n-species competition system. This chapter will put com-petition model with impulsive into competition model with non-impulsive. By using impulsive inequalities, we obtain permanent of the system. By construct-ing a suitable Lyapunov function and using some analysis techniques to obtain asymptotic stability and uniqueness of almost periodic solution of the system.In Chapter 4, we discuss the existence of almost periodic solution for impul-sive 2-species Nicholson-Typem model. 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 inequali-ty to obtain the existence and exponential stability of the almost periodic solution of the system. The periodic solution in literature is extended to almost periodic solution.