Almost Periodic Solutions For Several Kinds Of Biological Models With Impulses 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 consisted of four chapters.In Chapter1, we introduce issues arising from the historical background and main tasks of this article.In Chapter2, we discuss the existence of almost periodic solution for im-pulsive2-species Logarithmic population model with time-varying delay. Our approach is based on the estimation of the Cauchy matrix of the corresponding linear impulsive differential equations. We employ the contraction mapping prin-ciple 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 Chapter3, we consider the existence of almost periodic solution for im-pulsive Volterra model with mutual interference and Beddington-DeAngelis func-tional response. By constructing a suitable Lyapunov function and using some analysis techniques, we obtain some sufficient conditions which guarantee ex-istence of a unique positive almost periodic solution of the system. By using impulsive inequalities, we obtain permanent of the system.In Chapter4, the almost periodic solution of n-species Gilpin-Ayala com-petition system with delays and feedback controls is discussed. 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,the permanent of the system is obtained.