On Cluster Synchronization Control Methods For Complex Networks

The synchronization of complex networks originates from many fields such as physics,chemistry,engineering technology,sociology and so on.In recent years,almost all researches on cluster synchronization control for single-coupled complex networks are assumed that the number of external nodes is less,and then,the existing pinning strategy is not suitable for networks with a large number of external nodes such as neural networks.Therefore,it is necessary to propose a new pinning strategy.At the same time,most of the current research is for a single-coupled network.It is rarely considered that there are cooperation and competition between communities such as communication networks.So it is significant to study cluster synchronization control problem for competitive-cooperative complex networks in the real world.In this thesis,the cluster synchronization of complex networks is investigated based on the Contraction theory,Lyapunov stability theory and matrix theory.The main work can be summarized as follows:Firstly,we studied the cluster synchronization problem for the single-coupled network with a large number of external nodes.In this model,coupling terms in the same community and among different communities are described separately in matrix to clearly illustrate the network.Based on the cluster-input-equivalence condition,the pinning nodes are selected and the synchronization controller is designed.Contraction theory is used to obtain the sufficient condition of cluster synchronization in the single-coupled network.Taking the FN neuronal oscillators network system coupled by three communities as a simulation example,the numerical simulation results show that the single-coupled network can be cluster synchronized by the designed controller.In addition,it shows that the pinning strategy based on the cluster-input-equivalence condition is more effective than just pinning external nodes.Secondly,on the basis of a single-coupled complex network and considering the diversity of the coupling relationship between communities,we studied the cluster synchronization problem for the competition-cooperative complex network.In this network,the nodes in the same community interact through the same type of connection and those in different communities interact through different types of connections.Then a synchronization controller is designed with pinning control strategy basing community detection algorithm and degree centrality.Lyapunov stability theory is used to obtain the sufficient condition of cluster synchronization in the competition-cooperative network.Taking the scale-free network and the small world network separately as a simulation example,the result shows that the competition-cooperative network can be cluster synchronized by the designed controller.In addition,increasing the scale of the network,it shows that degree centrality is more relevant to the cluster synchronization of competition-cooperative complex networks than betweeness centrality,closeness centrality and eigenvector centrality,and combined with community detection algorithm can shorten the synchronization time.Finally,the main work of this thesis is summarized,and some future research directions are put forward.