Effects Of Multiple Coupling Modes On Synchronization Of Multi-layer Networks

Multilayer network model is more consistent with the structure and mechanism of many real systems,and can describe the morphology,function and development trend of some real systems more accurately and comprehensively.It is a very effective method to study the complexity problem.Synchronization is one of the key research branches of complex network theory,which has been widely used in biology,power,transportation and communication.At present,great academic achievements have been made in the research on the synchronization of complex networks.At the same time,the research trend of complex network gradually expands from single layer network to multi-layer network.In this paper,the eigenvalue spectrum and its synchronization capability of multilayer star networks under different coupling modes are studied and three kinds of multilayer star network models are constructed.Then,the super-Laplacian matrix of each multilayer network model is written,and its eigenvalue spectrum is derived strictly.According to the main stability function method,the effects of coupling modes and network parameters on the network synchronizability are studied respectively.Finally,the mechanism of system synchronization is studied by applying specific dynamics to the nodes.Our conclusions are as follows: for multilayer star networks with different bidirectional coupling strength,when the synchronous domain is unbounded,it is actually the coupling strength of aggregation that affects the network synchronizability,while when the synchronous domain is bounded,the bidirectional coupling strength will affect the network synchronizability in different ways.If the multilayer star network contains multiple hub nodes in each layer,the number of hub nodes always has a crucial impact on the network synchronizability,increasing the number of hub nodes can effectively improve the network synchronizability,but at the same time,the inter-layer coupling of hub nodes is adverse to the realization of network synchronization.When the total value of intra-layer coupling strength is constant and some of them changes,the remaining coupling strength will changes in the opposite trend,and the variation trend of network synchronizability is always the same as that of the smaller coupling strength.Moreover,when the synchronous domain is bounded,the network has a strong synchronizability and is easier to realize synchronization.Finally,the hybrid synchronization of the single-driven and multi-responsechaotic system is realized by designing the controller and the adaptive law of parameters,and the unknown parameters in the system are estimated accurately.