Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions
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AbstractIn this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.
Acceptance Date21/10/2020
All Author(s) ListJin-Long Liu, Zu-Guo Yu, Yee Leung, Tung Fung, Yu Zhou
Journal nameChaos
Year2020
Month11
Volume Number30
PublisherAIP Publishing
Place of PublicationNew York
Article number113123
ISSN1054-1500
eISSN1089-7682
LanguagesEnglish-United States
Keywordsfractal analysis, recurrence networks, 2D fractional Brownian motions

Last updated on 2021-19-09 at 23:36