Stability Of The Delayed Neural Network Models With Small World Connections

Artificial neural network is one of the hot research topics in recent years. It has achieved prominent progress in the theory and application.In this paper, the development history and models of the artificial neural network system are first introduced, and then the actual application and research results are also summarized. Secondly the neural network systems with time delays are introduced and the characteristics of the differential difference equations are introduced.This paper considers the neural network models with small world connection.Therefore, we introduce the concept, the model and the main characteristics of the complex networks. This paper focuses on the following problems:(1) presents a detailed analysis on the dynamics of a ring network with small world connections. On the basis of Lyapunov stability approach, the global stability criterion with time delay is investigated.(2) Then presents a detailed analysis on the local stability of a ring network with small world connections. By using the perturbation theory of matrix, we give the upper and lower bounds of maximum and minimum eigenvalues of the coupling strength matrix, and then give the generalized sufficient conditions that guarantee the system complete stability or complete instability. In paper with mean-field theory. It indicates that our result is a more conservative stability condition than that in the mean-filed theory. However, the proposed method can give the conditions that system is completely stable. At the end of the article, we summarize the thesis, and the feature research work is prospected.