Stability And Synchronization Analysis For Several Kinds Of Neural Networks

During the recent years,artificial neural networks have always been an object with immense attention due to their specific self-learning ability,which makes neural networks have been extensive applied in combinatorial optimization,signal processing,parallel computing,and some other fields.However,these widespread applications of neural networks are practically based on their affluent dynamic properties in theory,including stability,synchronization,dissipativity,chaos,etc.Therefore,the theoretical investigation about the dynamic behaviors of different neural networks is important.In this dissertation,the stability and synchronization of several kinds of neural networks are studied.By using matrix measure method,the theory of differential equation with deviating argument,event-triggered control and Lyapunov function method,according to the characteristics of corresponding neural networks,some theoretical criteria of the stability and synchronization are obtained.The main contents of this paper are summarized as follow:The exponential stability of a class of complex-valued neural networks with deviating arguments is studied.By decomposing the considered complex-valued neural networks into its real and imaginary parts and then combining them in a matrix form,an equivalent 2n-dimensional real-valued neural networks is obtained.The Lyapunov function is no longer required,based on the matrix measure method and the theory of differential equation with deviating argument,some sufficient conditions are firstly derived to ascertain the addressed system to be exponentially stable under different activation functions.The problem of exponential synchronization for complex-valued neural networks with advanced and retarded arguments is investigated.Based on the concept of driveresponse,the synchronization error system is constructed.After designing the feedback controller reasonably,the sufficient conditions for realizing the global exponential synchronization between drive response systems are obtained.The exponential synchronization of a class of memristive neural networks with discrete and distributed time-varying delays is discussed.An event-triggered controller with the static and dynamic event-triggering conditions is designed to improve the efficiency of resource utilization.By constructing a new Lyapunov function,the exponential synchronization of the memristor neural networks is realized under the designed event-trigered controller.In addition,the Zeno behavior will not occur by proving that the event-triggering interval have a positive lower bound under different event-triggering conditions.The basic theories of stability and synchronization on several kinds of neural networks are analyzed,especially the appropriate methods are used to analyze the corresponding networks,which further strengthen the ability of neural networks in practical application.