Study On The Input-to-state Stability Of Neural Networks With Infinite Delays

In the past decades,neural networks have attracted much attention by many scholars because of its wide applications in many fields.Since stability is the precondition of neural networks,it is important to study the stability of neural networks.Input-to-state stability,which is an extension of stability,is a concept that considers the stability of systems with additional input noise.Thus it is one of the characteristics that can not be ignored.In addition,there are a large number of factors that affect the stability of neural networks in real life,such as time delay,impulses,random noise,fuzzy algorithm and etc.Each kind neural networks have some well known results,but there is few investigation on infinite delay.Infinite delay is a further generalization of bounded delay to make it more general.Based on this,this thesis mainly from the following three aspects of research:In the first part,we study the p-moment input-to-state stability of the bidirectional association memory neural networks with infinite time delay and Brownian motion.By extending the corresponding Hanalay-type delay inequality,constructing the new Lyapunov general function,and combing with the It(?) formula,two sufficient conditions which guarantee the input-to-state stability of the desired model are given.Finally,the reliability of our conclusions is illustrated by numerical examples and simulation diagrams.In the second part,it considers the p-moment input-to-state stability of the bidirectional association memory neural network with infinite time delay and Markov jumping.By using the Halanay inequality,applying the Lyapunov stability,combing with the It(?) formula,we give the sufficient conditions that determining the p-monment inputto-state stability of the model under consideration.Finally,some simulation numerical examples are provided to demonstrated the effectiveness of our criterion.In the third part,the exponential input-to-state stability of the impulsive stochastic fuzzy Cohen-Grossberg neural networks with infinite time delay was considered.By generalizing delay differential inequalities,constructing a new Lyapunov function,some sufficient conditions ensuring the mean-square exponential input-to-state stability of our considered Cohen-Grossberg neural networks are obtained.Finally,numerical simulation examples are given to verify the validity of our conclusions.