Chaotic Synchronization In A Multi-Layer Network

In nature,synchronization can be found everywhere.Scientists have conducted in-depth research on synchronization and applied the results of synchronization research in the fields of physics,biology and economics.With the rapid development of complex network science,more and more people are combining the research of dynamic systems with complex networks.In recent years,research on dynamic systems in complex networks has become a hot issue.In this paper,we mainly study the synchronization behavior of the lorentz oscillator subsystem on a two-layer network.We introduce switch coupling into the system,and control the switching frequency of the vibration subsystem on the two-layer network and the time ratio of each layer network in the system by controlling the two control parameters of the switch coupling.It is found that the critical time proportion of system synchronization has little relation with the switching frequency when the switching frequency is large.When the switching frequency is small,the critical time ratio of synchronization is closely related to the switching frequency and the coupling strength of the system.In order to explain the above interesting phenomenon,we proposed the equivalent coupling analysis method and carried out specific analysis.Through the study of the dynamic behavior on the constructed new two-layer network,it can be seen that our analysis method has certain universality.