Global Exponential Stability Of Several Cellular Neural Networks With Delays

Cellular neural networks with various types of delays have been extensively studied since its applications in picture processing, pattern recognition and associative memories. The stable networks with response time maybe in practice, therefore, the study of the stability of cellular neural networks with delays is very valuable.This article discusses the global exponential stability of several delayed cellular neural networks. Firstly, in the introduction the research background and history of the development of neural networks, a brief introduction and current situation of researches of cellular neural network were introduced. Secondly, global exponential stability of cellular neural networks with constant delay is studied and a sufficient condition of globally exponentially stable is investigated. In previous studies, most of the results depend on constructing a suitable Lyapunov function to analyze the stability. However, the conclusion was obtained by using the method of inequality analysis and Holder inequality. Thirdly, the global exponential periodic of a class of generalized cellular neural networks with distributed delays and periodic input was studied by constructing Lyapunov functional and Ilalanay-type inequality. The easy-to-verify sufficient conditions which are ensuring the every solution of the networks exponentially converge to the unique periodic solution were gained. Finally, the article discusses the exponential stability of a class of cellular neural networks with multi-pantograph delays. By using the method of nonlinear measure, the suilicient conditions of global exponential stability was obtained and gave the exponential convergence rate of the solution. In each section giving the corresponding examples and simulation results are given to verify the correctness of the results.