Research On The Existence Of Anti-periodic Solutions And Anti-synchronization For Two Types Of Neural Networks

With the rapid development of computer computing functions,the theoretical research of artificial neural networks has gradually fallen into practice,solving difficult problems in engineering fields such as signal processing,expert systems,robot control,optimization and prediction.In recent years,a large number of excellent results have emerged to study the stability and synchronization of neural networksThis dissertation focuses on the existence and global exponential stability of antiperiodic solutions of time lag neural networks with inertial terms and investigates the finite-time inverse synchronization of two types of time lag neural networks.The work of this paper is organized into four chapters,and the primary studies are as follows:In the first chapter,the development of neural networks and the latest research results are introduced,then the challenges of time lag,periodicity,and synchronization phenomena on the dynamics of neural networks are introduced,and the existing research results are analyzed,and finally,the research significance and innovation points of the work done are discussed.In Chapter 2,the existence of anti-periodic solutions for general delayed bidirectional associative memory neural networks with inertial terms and global exponential stability are explored with the help of variable substitution,based on coefficient fundamental solution matrices and suitable Lyapunov general functions.Complementing some existing studies,the obtained results are new.The validity of the obtained results is verified by examples.In Chapter 3,distinguishing from traditional analysis techniques,a novel mathematical analysis is introduced without resorting to the established finite-time stability theorem,a proper state controller is designed,a criterion for finite-time antisynchronization of time-lag general BAM neural networks in the drive-response framework is established,and the obtained results extend and improve the conclusions of the existent literature.The soundness of the obtained theoretical results is verified by a numerical example.In Chapter 4,a new criterion for realizing finite-time anti-synchronization of timelagged competing neural networks with different time scales is established by designing a suitable state controller and introducing a novel mathematical analysis method to simplify the computation,drawing on the research method in Chapter 3,without resorting to the finite-time stability theorem,and the obtained results extend and improve the conclusions of the existing literature.In the end,the validity of the derived theoretical results is verified by giving a numerical example.Figure [2] Reference [99]...