Study On Synchronization And Identifications Of Parameters And Topology Of Time-varying Network Group Constituted By Chaotic Systems As Nodes

It is well-known that the complex networks are of very comprehensive applications in many fields,such as WWW,Internet,neural network,and so on.Therefore,the investigation on complex network is in the ascendant in recent years,including the modeling of complex network,the design of synchronization and the identification of parameter and topology,etc.So far,the researches on complex network focus mainly on the unchanged topology structure.In the actual applications,however,there exist the links among many sub-networks to further construct a network group structure.For example,the global area network(GAN)is constituted by the local area networks(LAN).Meanwhile,the number of nodes may be added or reduced,and links between nodes may also remain dynamic varying,which causes that the topology of network group will be changing from time to time.So,it is of better academic value and application prospect to investigate the synchronization,parameter identification and topology identification of time-varying network group in depth.The main contents of this thesis are as follows:Firstly,some superchaos dual-ring erbium-doped fiber laser systems are chosen as nodes to construct four complex subnetworks with diverse topologies,and then further to form a time-varying network group.Based on the Lyapunov stability theorem,the synchronization principle of time-varying network group is designed optimally and the general expression of node controller is given.The simulation results show that the real-time synchronization among all subnetworks with different structures within the network group can still be realized although the topology of the network group keeps changing,indicating that the designed synchronization principle is reasonable and efficient.Secondly,some Haken-Lorenz laser chaotic systems are chosen as nodes to construct a time-varying network group including four complex subnetworks.Based on the Lyapunov function,the node controller and the parameter identification law are designed theoretically.The simulation results show that not only the topology changing of the network group can be tracked quickly and the real-time synchronization of the time-varying network group is further realized,but also the unknown parameters in the node dynamic equations can be identified accurately.Finally,some Lü chaotic systems are selected as nodes to construct four complex subnetworks with diverse topologies,and then further to form a time-varying network group.Especially,the topology of the network group(including the inner and outer coupling matrix elements)is uncertain.Similarly,the reasonable node controller and the identification laws of the inner and outer coupling matrix elements are designed based on the Lyapunov function.Based on the Lyapunov function,the node controller and the parameter identification law are designed theoretically.The numerical results show that the synchronization among all subnetworks with diverse topologies within the time-varying network group is realized quickly,and the coupling matrix elements(topology of network group)are also identified accurately,which implies the synchronization principle of the time-varying network group and the identification law of topology are effective.At present,it is a hot topic about the investigation of time-varying network group.But some corresponding theories and techniques are still immature yet.Therefore,it is of important significance to research on the synchronization technology and parameter and topology identifications of time-varying network group in depth.It is hope that the preliminary results in this work can provide some valuable references for the investigation and development in complex network field.