Persistent excitation in adaptive parameter identification of uncertain chaotic system

This paper studies the parameter identification problem of chaotic systems.Adaptive identification laws are proposed 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.     

基于格兰杰因果网络的中美贸易战对上证行业冲击的研究

中美贸易战对行业冲击是普遍关注的问题,本文选取2016年8月—2019年10月的上证行业指数,构建了格兰杰因果关系网络,然后结合事件分析法对风险传播模型的参数进行估计,最后利用蒙特卡罗算法模拟行业受到贸易战冲击后金融风险传播情况,并计算贸易战发生前后的上证股市金融网络风险传播的基本再生数.研究发现:第一,贸易战明显改变了上证行业关系结构,行业指数之间联系变得更为紧密;第二,贸易战发生初期,受美国加征关税影响,上证股市感染节点数量迅速增加,并且感染规模会在第10—15个交易日内达到峰值,感染节点数量大约在第25个交易日后开始趋于平缓,市场逐渐恢复;第三,基本再生数计算结果表明,上证股市在贸易战发生初期金融风险传播较快,上证股市容易产生“同涨同跌”的现象.     

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.     

复杂动力网络的鲁棒性同步

本文研究了扰动下复杂动力网络的同步问题. 利用输入状态稳定性分析的方法, 给出了鲁棒同步的概念, 分析了非时间延迟的和含有时间延迟动力网络的同步, 数值仿真也验证了结果的有效性.     

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

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.     

Explosive synchronization of complex networks with different chaotic oscillators

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 Rssler 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.     

Comparison of Phase Synchronizability of Several Regular Networks for Non-Phase-Coherent Attractors

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.