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

TL;DR

This paper investigates how network topologies derived from time series exhibit a period-doubling cascade to chaos, using motif analysis and a refined recurrence-based network approach to connect phase space structures with network features.

Contribution

It introduces a refined network construction method based on k-nearest neighbors and motif analysis to explore the period-doubling route to chaos in dynamical systems.

Findings

Network motifs reveal the period doubling cascade process.

Refined network construction enhances detection of chaos transition.

Links phase space topology to network topology.

Abstract

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.