Research On The Stability,Synchronization And Application Of Several Kinds Of Complex Dynamic Networks

Complex dynamical networks exist widely in the real world,which is a multidisciplinary research object that combines nonlinear systems,graph theory,control theory,biology,physics and mathematical theory.Each node that constitutes a complex dynamic network can be regarded as a nonlinear system,and there are various complex links between the nodes.The commonly used traffic network,power network,neural network and so on are all complex dynamic networks.The stability,synchronization,propagation and game behaviors in complex dynamic networks can bring various beneficial or unfavorable effects to our life.So it has become one of the hotspots in the present search.This paper mainly studies the stability and synchronization problem of serveral kinds of comlex dynamic networks,including a kind of complex dynamic network with multilinks,a kind of neutral-type neural network with mixed delays,and three kinds of memristor-based fractional-order neural networks.Moreover,we also study the application of synchronization of a kind of coupled recurrent neural network in parameters identification.The innovative work of this paper is presented as follows:1.Two kinds of synchronization control problems for complex dynamic network with multilinks are studied.The first one is the finite-time synchronization control of complex dynamic network with delay based on intermittent control.By designing a suitable intermittent controller,constructing a suitable Lyapunov function and using the Lyapunov stability theory,the sufficient conditions for the drive-response systems to achieve the finite-time synchronization can be obtained and the settling time can be calculated simply.The second one is the generalized decay synchronization problem of the complex dynamic network with multilinks and time-varying delays.According to the definition of y/-type stability,the definition of generalized decay synchronization of drive-response systems is given.By defining a new nonlinear feedback controller and constructing a new Lyapunov-Krasovskii function,we deduce the synchronization criterion that can ensure the drive-response systems to realize the generalized decay synchronization.2.For the stability and synchronization control problems of a kind of neutral-type neural network,we have done two works.The first work is based on the definition of the finite-time stability,rather than the Lyapunov stability theory,and studies the finite-time stability problem of the neutral-type neural network with discrete time-varying delays,finite distributed delays,infinite distributed delays,and neutral-type delays,and a series of sufficient conditions are derived;The second is the extension of the first work.The global fixed-time synchronization problem of coupled neutral-type neural network with mixed delays is investigated.By defining a suitable feedback controllers and Lyapunov function,we obtain sufficient conditions for easy verification to ensure the drive-response systems to achieve the global fixed-time synchronization.3.For a kind of memristor-based fractional-order neural network,we study the stability and synchronization control problem of three different network models.The first network model is memristor-based fractional-order Cohen-Grossberg neural network.With the help of memristor mathematical model,the definition of Caputo fractional-order calculus,set-valued map,differential inclusion theory and Gronwall inequality,the switched fractional-order differential equations with discontinuous right-hand side are converted into ordinary fractional-order differential equations,and then according to the the definition of finite-time stability,we derived the finite-time stability conditions of the proposed model,and obtain the synchronization criterion of drive-response systems through a simple linear feedback controller;The second network model is the memristor-based fractional-order delay neural network.By adopting a method similar to the first model,and using the Gronwall-Bellman inequality,Voltera intergral equation,we obtain the finite-time projective synchronization criterion of drive-response systems,analyze the feasible region where the system reaches the settling time,and extend the conclusion of projective synchronization to the complete synchronization and anti-synchronization;The third network model is the memristor-based fractional-order fuzzy cellular neural network,which incorporates memristor model,fractional-order calculus and fuzzy logic operation simultaneously,so that this model has more complex dynamic behaviors.According to the definitions of finite-time stability and synchronization,Banach fixed-point theorem,Gronwall-Bellman inequality and fuzzy logic,the sufficient conditions for the existence of the solution,the finite-time stability and synchronization of drive-response systems are obtained.4.The application of a kind of coupled recurrent neural network in parameter identification is discussed.By designing a simple adaptive controller and parameters update rules,the model parameters are estimated according to the network nodes to achieve the synchronization.The estimated parameters include not only adaptive parameters and connections weights,but also all the coupled parameters.Compared with some existing parameter identification results,this job is more general.