Dynamical Analysis Of Several Classes Of Delayed Neural Network Models

Since artificial neural networks have been advanced, the research of theory andapplication have been developed in high-speed. The dynamical behavior analysis ofneural networks has attracted the attention of many researchers and experts, dueto it plays important role in several areas such as associative memory, optimization,signal and image processing and pattern recognition. To date, numerous resultsconcerning the problems in dynamical behavior of artificial neural networks havebeen obtained. This paper studies the existence and uniqueness of equilibriumpoint and the global exponential stability of three classes of neural network modelsby constructing Lyapunov functional and applying inequality analytic techniques.Our results are independent of delays and are easy to realize. Therefore, our workhas preferable significance of theoretical instruction.The paper has four parts:In the first chapter, the background, significance, development history and thecurrent research situation for the study of artificial neural networks are presented.Then, the main work of this paper is brie?y introduced.In the second chapter, we discuss a discrete-time analogue of a class of con-tinuous time delayed cellular neural networks. We get several sufficient conditionsfor the existence of equilibrium point and the global exponential stability by ap-plying Banach's fixed point theorem and analytic techniques. Through computersimulations, it is easy to see that the discrete time system has a good imitation ofthe continuous systems.In the third chapter, we study the global exponential stability of a class ofgeneralized neural networks. We get several su?cient conditions for the existence ofequilibrium point and the global exponential stability by constructing Lyapunovfunctional and applying Brouwer's fixed point theorem, Halanay inequality andanalytic techniques. The results obtained are independent of delays and are easyto realize. Our work makes extension to the existent paper, that is, the conclusionsof existent paper are just a special case of our research. We give several examplesto verify the correctness and the applicability of our results.In the fourth chapter, we study the global exponential stability of a class ofgeneralized neural networks with continuously distributed delays. Several su?cientconditions which are independent of delays have been obtained by constructingLyapunov functional and applying analytic techniques and homeomorphism theory. These conditions have extended the results in some existing papers. At last, wegive several examples to illustrate the correctness and applicability of our results.