Research On Existence Of Almost Periodic Solutions For Several Kinds Of Differential Systems With Delays

The periodic and almost periodic of differential system with delay reflect the regular change of the system, they have attracted much attention. The almost periodic phenomenon is the most universal in this variation. It has been widely existed in mechanical vibration, celestial mechanics, power systems, economics, ecology etc. So, studying the properties of the solutions of differential equations has important practical significance. In recent years, the research of almost periodic solutions of differential equations not only in theory but also in practice get a lot of progress. Many researchers have applied their theories to the actual models, such as ecological models(Nicholson’s blowfliess Lasota-Wazewska、Lotka-VolterraLotka-Volterra system), neural network models, which contributes to the actual models in-depth understanding.In order to further understand the application of differential system, this dissertation separately discusses several types of differential equations with delays and impulsive effects, and delay effects. By means of different research methods, several kinds of the sufficient conditions of the systems existing almost periodic solutions have been obtained, and some examples are given. The full text structures are as follows:In chapter1, we simply offer the development and background for almost periodic so-lutions, delay differential equations, impulsive differential equations, meanwhile list the re-search method of almost periodic solutions. We will give the question which will be discussed and necessary prior knowledge in this dissertation.In chapter2, by using the contraction mapping fixed point theorem, we mainly discus the existence and stability of almost periodic solutions for two classes nonlinear impulsive delay systems, some sufficient conditions are given to the almost periodic solutions of these equations for ensuring their existence under some assumptions.In chapter3, a class of nonautonomous Lotka-Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka-Volterra system are obtained. In chapter4, we consider a class of almost periodic solutions for nonlinear impulsive neural networks with delay. By employing mathematical analysis techniques, some sufficient conditions for the existence and global stability of positive almost periodic solutions are obtained.In chapter5, as this paper’s end of part, we have summarized the paper and proposed several questions which were worth further Considering.