Delay Cohen-grossberg Neural Network Stability Analysis

Neural networks play an important role in signal and image processing, artificial intelligence and optimization. Recently, more and more attentions have been paid to the study of the dynamics of neural networks. The researches on neural networks for stability of equilibrium and periodic solution have been deepened (including asymptotic stability, exponential stability, absolute stability, periodic stability, and so on), and a series of significant results have been obtained. In the study of stability, the most common method is Lyapunov approach, which changes some stability into the functional stability defined on system trajectory properly. And through this function we obtain corresponding stability conditions, which can be divided into four expression forms at least, that is, the parameters of algebraic inequality, coefficient matrix norm inequality, matrix inequalities, linear matrix inequalities, and so on.In this paper, Lyapunov functional is proposed for analyzing the stability of delayed Cohen-Grossberg Neural Networks (CGNN). Global exponential stability conditions are obtained for the delayed CGNN when the nonconstant activating functions are monotone nondecreasing and Lipschitz continuous. This method also applies to the special model delayed cellular neural networks (DCNN), Hopfield neural networks (HNN) and delayed Hopfield neural networks (DHNN) of the delayed CGNN. We can also prove their global asymptotic stability and exponential stability. Comparing with other documents, we can find that the method of this paper can not only ensure the global stability of the equilibrium solution for various models, but also guarantee their global exponential stability. At the same time, the results of article [1] are extended for wider application.