Global Exponential Stability Of Three Categories Delay Neural Networks

This paper is concerned with the existence-uniqueness andglobal exponential stability of equilibrium point of a Hopfield neural networks, aimpulsive bidirectional associative memory neural networks and a fuzzy Cohen-Grossberg neural networks with mixed delays and reaction-di?usion, respec-tively.In Chapter 1, dynamical behaviors of a Hopfield neural networks withdistributed delays are studied. Firstly, the uniformly boundedness solution ofthe system is proved by inequality analysis technique. Then, using contractionmapping principle, the existence-uniqueness of equilibrium point of the system isgiven. Finally, a su?cient condition is obtained to ensure the global exponentialstability of the equilibrium point for the model. The results generalize the earlierpublications.In Chapter 2, the existence-uniqueness and the global exponential stabilityof equilibrium point of a impulsive bidirectional associative memory neural net-works with distributed delays are considered. Di?erent from the used methodssuch as Lyapunov functional, M-matrix theorem, our methods base on somebasic analytical technique, such as contraction mapping principle and di?er- ential inequality techniques to obtain the existence-uniqueness and the globalexponential stability of equilibrium point of the model.In Chapter 3, a fuzzy Cohen-Grossberg neural networks with mixed delaysand reaction-di?usion are discussed. By some inequality technique, the unique-ness of equilibrium point of fuzzy Cohen-Grossberg neural networks with mixeddelays and reaction-di?usion is proved. Then, a su?cient condition is given toensure the global exponential stability of the equilibrium point for this model.