Summary Recently, some existing works have introduced novel way to construct complex networks from embedded time series, which provides new sights into the organizational properties of the time series in phase space. In this paper, we attempt to answer the fundamental question of “how much information regarding the dynamic property of the original time series can be extracted from these networks.” To this end, we propose a new method for reconstructing time series from the networks. We compare the reconstructed time series from these networks and that from the recurrence plot. We find that these networks contain topological information of the embedded time series to a certain degree. In general, they are more powerful than the recurrence plot method in the reconstruction of embedded time series. In addition, we study a new generalized projective synchronization (GPS) of coupled complex dynamical networks with different sizes via feedback control and impulsive control. Based on the stability analysis of impulsive system, a network synchronization criterion is established. These works may find potential application for secure communication via networks.

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