Dynamical Systems Induced on Networks Constructed from Time Series

Entropy

Lvlin Hou⁴  Michael Small¹  Songyang Lao³  Guanrong Chen²  C.K. Michael Tse²  Mustak E. Yalcin²  Hai Yu² 

[1] School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia;id="af1-entropy-17-06433">1Logistics Academy, Beijing 100858, Chi;College of Information System and Management, National University of Defense Technology, Changsha 410073, China; E-Mails:;Logistics Academy, Beijing 100858, China

关键词: time series;    dynamical system;    complex network;    surrogates;   

DOI  :  10.3390/e17096433

来源: mdpi

【 摘 要 】

Several methods exist to construct complex networks from time series. In general, these methods claim to construct complex networks that preserve certain properties of the underlying dynamical system, and hence, they mark new ways of accessing quantitative indicators based on that dynamics. In this paper, we test this assertion by developing an algorithm to realize dynamical systems from these complex networks in such a way that trajectories of these dynamical systems produce time series that preserve certain statistical properties of the original time series (and hence, also the underlying true dynamical system). Trajectories from these networks are constructed from only the information in the network and are shown to be statistically equivalent to the original time series. In the context of this algorithm, we are able to demonstrate that the so-called adaptive k-nearest neighbour algorithm for generating networks out-performs methods based on ϵ-ball recurrence plots. For such networks, and with a suitable choice of parameter values, which we provide, the time series generated by this method function as a new kind of nonlinear surrogate generation algorithm. With this approach, we are able to test whether the simulation dynamics built from a complex network capture the underlying structure of the original system; whether the complex network is an adequate model of the dynamics.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.