Asymptotically Almost Periodic Solutions For Two Classes Of Cellular Neural Networks With Delays

Since a class of specific differential equations called cellular neural networks with delays have been established, the existence and uniqueness on all kinds of solutions for this class of equation become important study contents, especially the study on almost periodic type solutions.The existence and uniqueness of asymptotically almost periodic solutions for two classes of cellular neural networks are mainly studied in this paper, one is cellular neural networks with mixed delays, the other is cellular neural networks with changing delays. The whole paper is divided into four parts.The research purpose and significance of this paper are introduced in the first part, meanwhile, the origin of this subject, developing status and developing trend on the theories and related applications of almost periodic types functions are also introduced. The main contents of the dissertation paper are given at last.The contents of the second part are some basic theoretical knowledge. Some basic properties on almost periodic functions and asymptotically almost periodic functions are introduced. In addition, the related knowledge on exponential dichotomy is also introduced in this part. These basic theoretical knowledge can provide theoretical basis for main contents in chapter three and chapter four.The contents of the third part are about asymptotically almost periodic solutions of cellular neural networks with mixed delays. The existence and uniqueness of asymptotically almost periodic solutions on this class of cellular neural networks with mixed delays are discussed by using Banach fixed point theorem and related theoretical knowledge of almost periodic functions and asymptotically almost periodic functions.On the basis of the third part, asymptotically almost periodic solutions on a class of cellular neural networks with changing delays are discussed in the fourth part. By using Banach fixed point theorem and some knowledge on exponential dichotomy, combining with the research of almost periodic solutions on this class of cellular neural networks in some literature, the existence and uniqueness of asymptotically almost periodic solutions on this class of cellular neural networks are discussed.