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Entropy 2015, 17(9), 6433-6446; doi:10.3390/e17096433

Dynamical Systems Induced on Networks Constructed from Time Series

1
College of Information System and Management, National University of Defense Technology, Changsha 410073, China
2
School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia
*
Author to whom correspondence should be addressed.
Academic Editors: Guanrong Chen, C.K. Michael Tse, Mustak E. Yalcin, Hai Yu and Mattia Frasca
Received: 1 July 2015 / Revised: 15 September 2015 / Accepted: 16 September 2015 / Published: 18 September 2015
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
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Abstract

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. View Full-Text
Keywords: time series; dynamical system; complex network; surrogates time series; dynamical system; complex network; surrogates
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hou, L.; Small, M.; Lao, S. Dynamical Systems Induced on Networks Constructed from Time Series. Entropy 2015, 17, 6433-6446.

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