| In the field of the complex network research,synchronous phenomena are favored by many scholars because of their typical dynamic behaviors.In the process of synchronization,there are many variables,especially the node number of the network,the dynamic difference of nodes and the existence of uncertain factors in the connection process,that will affect the process of network synchronization.In view of the practical application value of network synchronization,this thesis will discuss the synchronization of uncertain networks with different number of nodes.In the first and second chapters of this thesis,the research background of complex network and some basic concepts,basic models and main contents of the thesis are briefly summarized.On the basis,this thesis introduces the knowledge of network synchronization in detail,including the definition,research significance and status,and determination method of network synchronization.Subsequently,the type of network synchronization and the spatiotemporal network are briefly described.In the third chapter,we discuss the exponential external synchronization problem of uncertain spatiotemporal networks with different node numbers.First,through constructing a reasonable controller based on Lyapunov theory,not only can a class of uncertain spatiotemporal networks with different nodes be tended to synchronization gradually,but also the adaptive law of coupling matrix elements describing the topology structure and feedback intensity can be determined.Finally,the spatiotemporal networks constituted by the one-dimensional Burgers systems and Logistic systems are taken as example for the simulation.The results show that the whole network presents stable exponential external synchronization and the synchronization speed depends on adjustable parameters.In the fourth chapter,the synchronization objects involved in the synchronization scheme of the third chapter are extended from continuous uncertain spatiotemporal networks to discrete uncertain spatiotemporal ones and the projective synchronization problem of spatiotemporal networks with uncertain scale factors are further discussed.Firstly,the projective synchronization of discrete uncertain spatiotemporal networks with different node numbers is realized by designing appropriate controllers.At the same time,the configuration matrix elements of the topology,scale factor and feedback strength are determined.Lastly,one dimensional ring cavity laser model and electro-optic two-way coupling lattice model areselected as the spatiotemporal network forms and chosen as an example to be simulated.It is found that the scheme can effectively control the network synchronization and synchronization performance is very stable.The fifth chapter makes a brief summary of the research contents in this thesis,and the outlooks of the future research content and direction are forecasted. |
