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

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.