  In this work, the topologies of networks constructed from time series from an
underlying system undergo a period doubling cascade have been explored by means
of the prevalence of different motifs using an efficient computational motif
detection algorithm. By doing this we adopt a refinement based on the $k$
nearest neighbor recurrence-based network has been proposed. We demonstrate
that the refinement of network construction together with the study of
prevalence of different motifs allows a full explosion of the evolving period
doubling cascade route to chaos in both discrete and continuous dynamical
systems. Further, this links the phase space time series topologies to the
corresponding network topologies, and thus helps to understand the empirical
"superfamily" phenomenon, as shown by Xu.
