非线性时间序列的复杂网络分析

Nonlinear time series analysis by means of complex networks

近十多年,运用复杂网络的方法进行时间序列分析,是非线性动力学发展的最新方向,为传统的以混沌理论为基础的非线性时间序列分析注入了新生力量,在刻画动力系统非线性特征方面,提供了很多崭新的见解,在很多不同领域内都取得了广泛应用.本文回顾三种主要的方法:递归网络、可视图以及转换网络.着重介绍三种网络方法的理论基础和各自的最新进展.本文将指明今后时间序列网络方法的发展方向,并为实际数据分析提供指导作用.

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.