Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic o...Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldu J M, Sendifia-Nadal I, Goemez-Gardefies J, Arenas A, Moreno Y, Goemez S, Jaimes-Reaitegui 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 R6ssler 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.展开更多
Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems, it does not work well for phase synchronization. Moreover, it is difficu...Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems, it does not work well for phase synchronization. Moreover, it is difficult to identify phase synchronization with the angle of rotation for non-phase-coherent attractors. We employ the recurrences plot method to detect phase synchronization for several regular networks with non-phase-coherent attractors. It is found that the coupling strength μ is different for different coupled networks. The coupling strength μ is reduced as completed coupled network scale enlarges, the coupling strength μ of star coupled network is irrelevant to network scale, and these two regular networks are easier to achieve phase synchronization. However, for ring and chain coupled networks, the larger the phase synchronization couple strength μ is, the larger the network scale is, and it is more difficult to achieve phase synchronization. For same scale network, once ring coupled structure becomes a chain coupled structure, phase synchronization becomes much more difficult.展开更多
This paper studies the parameter identification problem of chaotic systems. Adaptive identification laws are pro- posed to estimate the parameters of uncertain chaotic systems. It proves that the asymptotical identifi...This paper studies the parameter identification problem of chaotic systems. Adaptive identification laws are pro- posed to estimate the parameters of uncertain chaotic systems. It proves that the asymptotical identification is ensured by a persistently exciting condition. Additionally, the method can be applied to identify the uncertain parameters with any number. Numerical simulations are given to validate the theoretical analysis.展开更多
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...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.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 61203159,61164020,11271295,and 11071280)the Foundation of Wuhan Textile University (Grant No. 113073)
文摘Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldu J M, Sendifia-Nadal I, Goemez-Gardefies J, Arenas A, Moreno Y, Goemez S, Jaimes-Reaitegui 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 R6ssler 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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60574045 and 70771084, and the National Basic Research Programme of China under Grant Nos 2006CB708302 and 2007CB310805.
文摘Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems, it does not work well for phase synchronization. Moreover, it is difficult to identify phase synchronization with the angle of rotation for non-phase-coherent attractors. We employ the recurrences plot method to detect phase synchronization for several regular networks with non-phase-coherent attractors. It is found that the coupling strength μ is different for different coupled networks. The coupling strength μ is reduced as completed coupled network scale enlarges, the coupling strength μ of star coupled network is irrelevant to network scale, and these two regular networks are easier to achieve phase synchronization. However, for ring and chain coupled networks, the larger the phase synchronization couple strength μ is, the larger the network scale is, and it is more difficult to achieve phase synchronization. For same scale network, once ring coupled structure becomes a chain coupled structure, phase synchronization becomes much more difficult.
基金Project supported in part by National Natural Science Foundation of China (Grant Nos. 11047114 and 60974081)in part by the Key Project of Chinese Ministry of Education (Grant No. 210141)
文摘This paper studies the parameter identification problem of chaotic systems. Adaptive identification laws are pro- posed to estimate the parameters of uncertain chaotic systems. It proves that the asymptotical identification is ensured by a persistently exciting condition. Additionally, the method can be applied to identify the uncertain parameters with any number. Numerical simulations are given to validate the theoretical analysis.
基金Project supported by the Key Project of Ministry of Education of China (Grant No. 2010141)the National Natural Science Foundation of China (Grant No. 61203159)
文摘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.
