Geometrical invariability of transformation between a time series and a complex network

Zhao, Yi; Weng, Tongfeng; Ye, Shengkui

doi:10.1103/physreve.90.012804

Cited by 39 publications

(21 citation statements)

References 34 publications

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“…Geometrical properties of time series can usually be preserved in network topological structures. Lots of methods have been developed to capture the geometrical structure of time series from complex network aspect such as cycle network [2], correlation network [40], visibility graph [14], recurrence network [41], isometric network [15] and many others. Among those methods, the visibility graph has a straight forward geometric interpretation of the original time series.…”

Section: Methodsmentioning

confidence: 99%

Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.

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Section: Methodsmentioning

confidence: 99%

Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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“…Proximity network methods include cycle networks [9], correlation networks [10] and, most prominently, networks based on proximity in phase space [11,12]. These algorithms map states from the time series, which are commonly the states of the embedded time series but can also be cycles from pseudo-periodic time series [9] or coarse grained amplitudes [13], and allocate edges between these states based on some measure of closeness or similarity.…”

Section: Proximity Networkmentioning

confidence: 99%

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

McCullough

Small

Stemler

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

144

121

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We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding.The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set. 1 arXiv:1501.06656v1 [nlin.CD] 27 Jan 2015Within the last ten years a novel approach to time series analysis has emerged whereby data is transformed into a complex network and then analysed using various measures from network science. The choice of transformation algorithm is critical in this process as different methods are inherently more effective at capturing certain aspects of dynamics and less effective at capturing others. In this paper we investigate a recently proposed algorithm known as the method of ordinal partitions. This computationally simple algorithm explicitly embeds temporal information in the network structure by partitioning the time series into a set of symbolic states which become network nodes, and then connecting these nodes based on the transition sequence present in the data. New in this work, we generalise the algorithm by introducing a time lag parameter for the elements in each partition, as is done in traditional methods of time delay embedding. Our results demonstrate that this new approach generates networks which are measurably sensitive to the dynamics present in the source time series, and has the potential to be useful as a tool for change point detection in continuous chaotic systems.

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“…Transformations in the opposite direction have been explored as well, i.e., construction of time series from complex networks [17], and criteria based on geometrical invariability [18] have been introduced to confirm that the dynamical character of time series is preserved when mapped into a complex network.…”

Section: Introductionmentioning

confidence: 99%

Persistent topological features of dynamical systems

Maletić

Zhao

Rajković

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

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A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicia complex preserves all pertinent topological features of the reconstructed phase space and it may be analyzed from topological, combinatorial and algebraic aspects. In focus of this study is computation of homology of the invariant set of some well known dynamical systems which display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the

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Geometrical invariability of transformation between a time series and a complex network

Cited by 39 publications

References 34 publications

Multifractality and Network Analysis of Phase Transition

Multifractality and Network Analysis of Phase Transition

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

Persistent topological features of dynamical systems

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