Synchronization Analysis In Fractional-order Multilayer Networks

As a ubiquitous phenomenon,the synchronization behavior of multilayer networks has attracted the attention and research of many experts and scholars.At the same time,the historical memory characteristics of the network play an important role in function.Fractional calculus,as an extension of the integer order,reflects this characteristic well.The thesis focuses on a two-layer network composed of fractional-order oscillators,and investigates the mesoscale collective dynamical behaviors and control problem of the network,i.e.,intra-layer synchronization and inter-layer synchronization and control synchronization.The content is mainly carried out in two aspects:First,according to the characteristics of the multi-layer network and the dynamic properties of the network synchronization solution,the necessary constraint conditions are firstly presented for achieving intra-layer synchronization and inter-layer synchronization.With the constraints,based on the Lyapunov stability theory and the fractional-order system theory,sufficient conditions for inter-layer synchronization and intra-layer synchronization are obtained respectively.Interestingly,the conditions cover the basic synchronization criteria bridging the relationship of interacting between the topologies,inner coupling functions and coupling strengthes of the intra-layer and the inter-layer.Finally,numerical examples are provided to further verify the theoretical results.Second,in view of the complex characteristics of the multilayer network structure and the connection between the layers have an important influence on the dynamics of the network,and it is not easy to achieve network synchronization only by adjusting the coupling strength itself.Here,from the perspective of connecting edges between layers,by designing a suitable control rate and using stability theory,the conditions for the network to achieve complete synchronization are derived.The results show that the synchronization can be realized as long as the parameterg_i is large enough.Finally,the content of the thesis is summarized,and some feasible questions are raised for future work.