Characterizing system dynamics with a weighted and directed network constructed from time series data

Sun, Xiaoran; Small, Michael; Zhao, Yi; Xue, Xiaoping

doi:10.1063/1.4868261

Cited by 77 publications

(40 citation statements)

References 33 publications

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“…However, important features of ordinal networks are naturally inherited and limited by the symbolic sequences that give rise to networks. Some of these properties of ordinal networks have already been implicitly discussed in previous works [10,25,26], but they still lack attention. An important limitation is related to the maximum number of connections for a node.…”

Section: Methodsmentioning

confidence: 99%

Characterizing stochastic time series with ordinal networks

Pessa

Ribeiro

2019

Phys. Rev. E

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Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to its simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting non-random behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth seismic activity caused by large earthquakes. arXiv:1910.01406v1 [physics.data-an]

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Section: Methodsmentioning

confidence: 99%

Characterizing stochastic time series with ordinal networks

Pessa

Ribeiro

2019

Phys. Rev. E

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“…In this case, depending on the specific rule employed to define the symbols, the entropy will capture different properties of the ordering of the values in the time series, and will give a different result when the data values are shuffled randomly. For computing the distance between SAT and insolation time series, several advanced approaches can be used, for example, each time-series can be mapped into a network (by using, e.g., recurrence21, visibility22, or symbolic networks23) and then, the dissimilarity of the two networks obtained can be computed24.…”

Section: Discussionmentioning

confidence: 99%

Identifying large-scale patterns of unpredictability and response to insolation in atmospheric data

Arizmendi

Barreiro

Masoller

2017

Sci Rep

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Understanding the complex dynamics of the atmosphere is of paramount interest due to its impact in the entire climate system and in human society. Here we focus on identifying, from data, the geographical regions which have similar atmospheric properties. We study surface air temperature (SAT) time series with monthly resolution, recorded at a regular grid covering the Earth surface. We consider two datasets: NCEP CDAS1 and ERA Interim reanalysis. We show that two surprisingly simple measures are able to extract meaningful information: i) the distance between the lagged SAT and the incoming solar radiation and ii) the Shannon entropy of SAT and SAT anomalies. The distance uncovers well-defined spatial patterns formed by regions with similar SAT response to solar forcing while the entropy uncovers regions with similar degree of SAT unpredictability. The entropy analysis also allows identifying regions in which SAT has extreme values. Importantly, we uncover differences between the two datasets which are due to the presence of extreme values in one dataset but not in the other. Our results indicate that the distance and entropy measures can be valuable tools for the study of other climatological variables, for anomaly detection and for performing model inter-comparisons.

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“…Complex networks have also been successfully employed for time series analysis [22][23][24][25][26][27]. Correlation graphs [28,29], recurrence graphs [30][31][32], and visibility graphs [33][34][35][36][37] have been shown to provide relevant information, for example, of early warning indicators of qualitative changes and abrupt transitions.…”

Section: Introductionmentioning

confidence: 99%

Quantifying sudden changes in dynamical systems using symbolic networks

et al. 2015

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We characterize the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time series we construct a network in which every node weight represents the probability of an ordinal pattern (OP) to appear in the symbolic sequence and each edgeʼs weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent, and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.

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Characterizing system dynamics with a weighted and directed network constructed from time series data

Cited by 77 publications

References 33 publications

Characterizing stochastic time series with ordinal networks

Characterizing stochastic time series with ordinal networks

Identifying large-scale patterns of unpredictability and response to insolation in atmospheric data

Quantifying sudden changes in dynamical systems using symbolic networks

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