Synchronization Analysis And Control For Multilayer Complex Networks

Nowadays,science and technology develop rapidly,and network technology is one powerful push to promote science and technology progress.Various networks surround our daily life,work and study,therefore,they attract lots of attention of researchers.Most studies of complex networks focus on the single-layer network,however,there exist interactions among networks in the real world.It is difficult to describe these interactions by the single-layer network model.Therefore,multilayer network models proposed in this thesis can represent more general cases.This thesis investigates the synchronization problems of several kinds of multilayer networks,and mainly includes the following aspects: pinning adaptive synchronization and impulsive synchronization of stochastic multiplex homogeneous networks,impulsive synchronization of multiplex heterogeneous networks,and pinning synchronization of stochastic multiplex heterogeneous networks.The specific contents can be introduced as follows:(1)For the multiplex homogeneous networks with time delays and stochastic perturbations,a virtual leader is firstly introduced,and a pinning adaptive control is adopted to the multiplex follower networks and the corresponding pinning adaptive strategy is further designed.By applying Lyapunov stability theory and stability theory of stochastic differential equations,the derivatives of Lyapunov functions along this kind of multiplex homogeneous network are analyzed,and the sufficient criteria are derived to guarantee that the multiplex follower networks can finally synchronize with the leader.(2)From the view of cost-saving,impulsive control scheme is utilized for a class of multiplex homogeneous networks with stochastic perturbations.According to Lyapunov stability theory and exponential martingale inequality,sufficient criteria of synchronization are derived for the multiplex homogeneous networks.In addition,a two-layer network,where the first layer is coupled by continuous switching topology and the second layer is coupled by impulsive switching topology,is proposed.The mode-dependent average dwell time method and the mode-dependent average impulsive interval method are applied to analyze the effect of switchings and impulses,respectively.Meanwhile,the sufficient criteria of synchronization are obtained for the two-layer network.Furthermore,a relationship among the average dwell time,average impulsive interval and switching modes is obtained.(3)For a class of delayed multiplex heterogeneous networks,leader-following mechanism is applied under two cases: one leader is introduced and multiple leaders are introduced.The multilayer follower networks are exerted the impulsive control,and the sufficient conditions of quasi-synchronization and quasi-containment control for leader-following multiplex networks are obtained.When there exist multiple leaders in the multiplex networks,the definition of jointly directed spanning tree is proposed to ensure the connectivity of the multiplex networks.(4)For a stochastic two-layer heterogeneous network model with mixed delays,a pinning control strategy is applied,and the sufficient conditions for achieving inter-layer synchronization are derived.Furthermore,the stochastic multiplex homogeneous networks model is extended to the stochastic multiplex heterogeneous networks model,and a virtual leader is introduced.Combining the pinning control strategy and the impulsive control strategy,only a fraction of nodes is exerted impulsive control,which further saves the control cost.Based on the stability theory of stochastic impulsive systems,the synchronization criteria of the stochastic multiplex heterogeneous networks and the upper bound of the error systems are obtained.