| From the view point of continuity of time,complex dynamical networks are divided into continuous-time complex dynamical networks and discrete-time complex dynamical networks.Compared with continuous-time complex dynamical networks,the discrete-time ones are more suitable to model digitally transmitted signals.As a significant collective behavior of networks,synchronization has attracted extensive attention from domestic and foreign scholars.Generally speaking,a network cannot achieve the desired synchronization state spontaneously,and control is an effective means to realize network synchronization.Thereby,it is very important to discuss the synchronization control of discrete-time complex dynamical networks.It is worth noticing that the nodes in realistic networks usually have almost same or similar characters,which are embodied by their intrinsic dynamics.In general,these similar characters,which are named as similarities in this thesis,will affect the synchronization behavior of nodes,and they can simplify the design of synchronization controllers for networks.In addition,the importance of nodes in real networks is not always same.There are usually a few nodes that are more important than the others in some sense,which are called as crucial nodes in this thesis.The similarities between the crucial nodes and other nodes are alse focuses on.It should be mentioned that the nodes discussed in this thesis can have different state dimensions,which can better describe the real networks.It should also be noted that realistic networks especially biology engineering networks usually have nonlinear inner coupling functions and inevitable time delays.Motivated by the above considerations,the control strategies are investigated for a few kinds of discrete-time complex dynamical networks with similar different-dimensional nodes in this thesis.The main contents of this thesis are as follows:（1）The matrix projective synchronization of a type of discrete-time complex networks with linear similar nodes is investigated.The network model is composed of nodes with different state dimensions and its outer coupling matrix is asymmetric.Besides,the existence of the crucial node is considered and the commonness between other nodes and the crucial node is introduced.Furthermore,based on the commonness and the Lyapunov stability theory,two control strategies are proposed to make the exponential matrix projective synchronization and the asymptotic matrix projective synchronization of our networks come true,respectively.（2）An asymptotic generalized synchronization scheme for a class of nonlinear discrete-time complex dynamical networks with different dimensional similar nodes is proposed.The network model is composed of nonlinear nodes with different dimensions.The overall coupling strength is time-varying and the inner coupling functions are allowed to be nonlinear.Based on the similarity of nodes anf the control method,a decentralized feedback control strategy is proposed to realize the asymptotic generalized synchronization of this class of networks.（3）An exponential generalized synchronization scheme for a type of nonlinear discrete-time complex dynamical networks with time-delay couplings is designed.The similarities between discrete-time nonlinear nodes with different dimensions are described quantitatively.The outer coupling matrix of the network is time-varying and the inner coupling functions are nonlinear and with time-varying delays.By the decentralized controllers put forward in this thesis,this kind of networks can realize exponential generalized synchronization. |
