Wavelet multiresolution complex network for analyzing multivariate nonlinear time series

Zhong-Ke Gao, Shan Li, Wei-Dong Dang, Yu-Xuan Yang, Younghae Do, Celso Grebogi

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Abstract

Characterizing complicated behavior from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. We in this paper propose a novel wavelet multiresolution complex network (WMCN) for analyzing multivariate nonlinear time series. In particular, we first employ wavelet multiresolution decomposition to obtain the wavelet coefficients series at different resolutions for each time series. We then infer the complex network by regarding each time series as a node and determining the connections in terms of the distance among the feature vectors extracted from wavelet coefficients series. We apply our method to analyze the multivariate nonlinear time series from our oil-water two-phase flow experiment. We construct various wavelet multiresolution complex networks and use the weighted average clustering coefficient and the weighted average shortest path length to characterize the nonlinear dynamical behavior underlying the derived networks. In addition, we calculate the permutation entropy to support the findings from our network analysis. Our results suggest that our method allows characterizing the nonlinear flow behavior underlying the transitions of oil-water flows.
Original languageEnglish
Article number175012327
Number of pages11
JournalInternational Journal of Bifurcation and Chaos
Volume27
Issue number8
DOIs
Publication statusPublished - Jul 2017

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Nonlinear Time Series
Multivariate Time Series
Complex networks
Multiresolution
Complex Networks
Time series
Wavelets
Wavelet Coefficients
Weighted Average
Water
Clustering Coefficient
Series
Network Analysis
Path Length
Two-phase Flow
Feature Vector
Dynamical Behavior
Shortest path
Permutation
Entropy

Keywords

  • nonlinear time series analysis
  • wavelet multiresolution
  • complex network
  • oil-water flows

Cite this

Wavelet multiresolution complex network for analyzing multivariate nonlinear time series. / Gao, Zhong-Ke; Li, Shan; Dang, Wei-Dong ; Yang, Yu-Xuan ; Do, Younghae; Grebogi, Celso.

In: International Journal of Bifurcation and Chaos, Vol. 27, No. 8, 175012327, 07.2017.

Research output: Contribution to journalArticle

Gao, Zhong-Ke ; Li, Shan ; Dang, Wei-Dong ; Yang, Yu-Xuan ; Do, Younghae ; Grebogi, Celso. / Wavelet multiresolution complex network for analyzing multivariate nonlinear time series. In: International Journal of Bifurcation and Chaos. 2017 ; Vol. 27, No. 8.
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