Stability Analysis Of Three Types Of Cellular Neural Networks With Delays

With the continuous development of artificial intelligence,the research of neural networks has come to a climax again and again.Among them,cellular neural networks have been widely used in many fields,such as:pattern recognition,connected piece detection,signal transmission and other fields.However,the speed is limited during signal transmission.Therefore,when analyzing the stability of the cellular neural network model,it is necessary to consider the time delay.This paper will study the stability of three types of cellular neural network models with delay,the main contents are as follows:Firstly,we introduce the background and significance of the topic,focusing on the development of neural networks and cellular neural networks.Secondly,chapter,we study a cellular neural network models with three time delays.The main research uses time delay as a parameter to analyze the influence of parameters on the stability of the model.By discussing the distribution of the eigenvalues of the relevant characteristic equations,it is proved that the model has stable transition and synchronous(asynchronous)periodic vibration under certain conditions.Next,the dynamic behavior of a cellular neural network models with unbounded delays is studied.By means of the properties of the matrix,a sufficient condition for the asymptotic stability of the cellular neural network model with unbounded delay is given.In the end,the global stability problem of a cellular neural network models with discrete and unbounded delays is studied.By constructing the appropriate Lyapunov functional and the theory of non-singular M-matrices,the sufficient conditions for judging the global asymptotic stability of the equilibrium point of the system are obtained.The sufficiency condition is to judge whether the matrix is a non-singular M-matrix,so it is very easy to verify.