The Stability Of Impulsive Delay Neural Network

In the last few decades, cellular neural networks have been extensively studied due to its many important applications in some areas, such as: pattern recognition, associative memory, image processing and so on. At the same times, a new neural networks pattern (BAM neural networks) has been extensively studied. However, stability analysis is an important problem of neural networks.In this paper, the global exponential stability and periodicity are investigated for the cellular neural networks with discrete and distributed delays. And the exponential stability conditions of a class of BAM neural networks with distributed delays and impulse are obtained.The main results are as follows:1.Exponential stability and periodicity are investigated for a class of cellular neural networks (CNNs) with discrete and distributed delays. Some sufficient conditions are derived for checking the exponential stability and periodicity for this system based on Lyapunov functional theory and dividing the state variables into subgroups according to the characters of the neural networks. These conditions are dependent on some blocks of the feedback matrix and the size of time delays.2.The exponential stability of BAM neural networks with distributed delays is discussed. In the condition of the signal transmission functions to be Lipschitz continuous, by constructing suitable Lyapunov functional, we derive several sufficient conditions for the globally exponential stability of the equilibrium point of the system.3.The global exponential stability conditions of BAM neural networks with distributed delays and impulse are derived. Using the Lyapunov stability theory and combing with differential inequalities with delays and impulses, several sufficient conditions are obtained for ensuring the system to be globally exponentially stable.