Qualitative Analysis Of Several Class Of Delayed Neural Network Models

Since neural networks were proposed, they have advanced with exceptionalspeed. For their great e?ectiveness on associative memories, optimal computation,automatic control, etc., the qualitative analysis of neural networks fixes a largenumber of experts's attention. By means of Lyapunov function, matrix theory,this paper analyzes the dynamical behaviors, including global stability of solution,existence and global attraction of almost periodic sequence solution, for severalclass of neural network models. The conditions what we give are independentof delays and easy to realize. Therewith, our work has preferable significance oftheoretical instruction.In the first part, we brie?y introduce the history and the current researchsituation of neural networks, and give a clean reins of the quality research. Throughciting and analyzing numerous works in this field, we also introduce the significanceof our subsequent researches, and give marks which will be used in our subsequentsections.In the second part, we have a research of a class of discrete delay Cohen-Grossberg neural networks. Through Brouwer's fixed point theorem, we get thesu?cient condition for existence of equilibrium point. By means of discrete Ha-lanay inequality lemma, we get su?cient conditions to guarantee the global ex-ponential stability of systems. Our work makes extension to the existent paper,namely, the conclusions of existent paper are just a special case of our research.The results obtained are independent of delays and easy to realized. Computersimulations verify the correctness of our result.In the third part, we discuss a discrete-time analogue of a class of continuous-time delayed cellular neural networks. Su?cient conditions are obtained for theexistence and global attraction of a unique almost periodic sequence solution thatis globally attractive through the inequality analysis technics, which is a extensionof existent papers, namely, generalizing the results without delays to the circum-stances containing delays. Through computer simulations, it is easy to see thatdiscrete time system has a good imitation of the continuous systems.In the fourth part, we analysis the global exponential stability of a class ofcontinuous time-varying delay cellular neural networks. Using Lyapunov-Krasovkiifunctional method, we get some su?cient conditions about the global exponentialstability of time-varying delay cellular neural networks. The results make exten- sion to the existent papers, namely, generalizing the results of constant delays tothe circumstances containing time-varying delays. To verify the correctness ande?ectiveness of our results, we give concrete computer simulation experiments.This paper makes strict theory proof, and gives concrete computer simulationexperiments. Not only do our results o?er superior theory instructions, but alsocan be easily implemented in actual systems . It has preferably consult values.