A method for quantifying the complexity of graph structures obtained from chaotic time series data

— Comparison with the lyapunov exponent and characteristics of graph structure —

Abstract

Complex phenomena are observed in various situations, and might be generated by deterministic dynamical systems or stochastic systems. Clarifying and analyzing complex phenomena is an important issue in the development of various technologies, such as control and prediction. In this study, we propose a method for quantifying the complexity of graph structures obtained from chaotic time series data based on Campanharo's method. Our results show that it is possible to quantify periodic, quasi-periodic, and chaotic states from the graph structure, and that numerical values show the same tendency as the Lyapunov exponent. Furthermore, we find that specific graph patterns are generated around the period-doubling bifurcation, which shows that our method can capture characteristic features of time series data that cannot be captured using the Lyapunov exponent.