In this work, the topologies of networks constructed from time series from anunderlying system undergo a period doubling cascade have been explored by meansof the prevalence of different motifs using an efficient computational motifdetection algorithm. By doing this we adopt a refinement based on the $k$nearest neighbor recurrence-based network has been proposed. We demonstratethat the refinement of network construction together with the study ofprevalence of different motifs allows a full explosion of the evolving perioddoubling cascade route to chaos in both discrete and continuous dynamicalsystems. Further, this links the phase space time series topologies to thecorresponding network topologies, and thus helps to understand the empirical"superfamily" phenomenon, as shown by Xu.
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机译:在这项工作中,通过使用高效的计算主题检测算法,通过不同主题的普遍性,探索了从基础系统按时间序列构建的网络拓扑,该周期经历了倍增的级联。通过这样做,我们采用了基于已提出的基于$ k $ nearest邻居递归的网络的改进方案。我们证明,网络结构的完善以及对不同主题的普遍性的研究,使得在离散和连续动力系统中,演化周期加倍的级联路径向混沌的方向全面爆发。此外,这将相空间时间序列拓扑链接到相应的网络拓扑,从而有助于理解经验的“超家族”现象,如Xu所示。
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