The three most widely used methods for reconstructing the underlying time series via the recurrence plots (RPs) of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.
Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Gómez-Garden es J,Gómez S,Arenas A and Moreno Y 2011 Phys.Rev.Lett.106 128701] and chaotic oscillators [Leyva I,Sevilla-Escoboza R,BuldúJ M,Sendin a-Nadal I,Gómez-Garden es J,Arenas A,Moreno Y,Gómez S,Jaimes-Reátegui R and Boccaletti S 2012 Phys.Rev.Lett.108 168702].Here,we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks.The continuous transition is discovered for Rssler systems in both of the above complex networks.However,explosive transitions take place for the coupled Lorenz systems,and the main reason is the abrupt change of dynamics before achieving complete synchronization.Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.
