Chaos Synchronization And Control On Double-layer Hypergraphs

Leader following synchronization is an important synchronization method,which refers to the presence of a leader in a network system.After a certain period of time,all agents in the network reach the same state as the leader.In real life,it is common for leaders to follow synchronization phenomena,such as aircraft formation flying and biological population migration.The control problem of leader following synchronization has received in-depth research in the past decade or so.However,there are few reports on discussing leader following synchronization in systems with high-order interactions.Furthermore,considering that containment control can effectively save costs,this thesis focuses on the study of leader following chaos synchronization and control on hypergraphs.Firstly,this thesis establishes a directed hypergraph dynamics model.In previous research work on leader following synchronization,it was generally assumed that the interaction between network nodes(system elements)was a point-to-point connection(i.e.,a connection between two nodes).However,many actual network connections do not only include point-to-point connections,but also include multi-node connections,i.e.,higher-order connections.A network with high order connections is called a high order network,and can usually be described by a hypergraph or simple complex.For example,brain neural networks,protein interaction networks,and so on are typical representatives of higher order networks.Secondly,in order to make complex dynamic networks more efficient and achieve global synchronization at a low cost,a containment control strategy is proposed.This strategy only controls a small number of nodes in the network.By using Lyapunov stability theory,the global stability conditions for directed hypergraph leader following synchronization are obtained.In addition,we provide a method for selecting constraint nodes,which minimizes the number of constraint nodes required for leader following synchronization in a directed hypergraph under fixed coupling strength.The effectiveness of the constraint strategy is verified using Chua’s circuit numerical values.Finally,considering that real-world network systems typically have multi-layer network structures.To this end,we further conducted optimization research on chaos synchronization and constraint control of double-layer hypergraphs.For example,a transportation network system is a multi-layer network system composed of aviation systems,railway systems,and highway systems,and a double-layer network is a typical representative of multi-layer networks.Almost all research methods and theories related to double-layer networks can be extended to multi-layer networks in parallel.We found that leader following synchronization can also be achieved for double-layer hypergraphs.In addition,with the help of the basic Laplacian matrix theory,we further explore the optimal selection of restraining nodes,and find that when only one node is controlled,priority control of the node with the largest degree of comprehensive nodes is most conducive to the synchronization of double-layer hypergraphs.The effectiveness of the strategy was tested using specific and randomly generated double-layer hypergraphs,respectively.