Nonlinear time series analysis by means of complex networks

Abstract

In the last decade, there has been a growing body of literatures addressing the utilization of complex network methods for the characterization of dynamical systems based on time series, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of three existing approaches of recurrence networks, visibility graphs and transition networks, covering their methodological foundations, interpretation and the recent developments. The overall aim of this report is to provide the Chinese readers with the future directions of time series network approaches and how the complex network approaches can be applied to their own field of real-world time series analysis.