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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.

Exploration of period-doubling cascade route to chaos with complex network based time series construction