Distinguishing Noise from Chaos: Objective versus Subjective Criteria Using Horizontal Visibility Graph

Ravetti, Martı́n Gómez; Carpi, Laura C.; Gonçalves, Bruna Amin; Frery, Alejandro C.; Rosso, Osvaldo A.

doi:10.1371/journal.pone.0108004

Cited by 82 publications

(61 citation statements)

References 81 publications

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“…This would open for the possibility to distinguish between the two process classes by determining the corresponding λ from the HVG degree distribution. However, Ravetti et al 18 provide ample numerical evidence which does not support this suggestion, and the classification based on the criterion seems unfeasible. To the best of our knowledge, there is no analytical expression for the degree distribution of correlated noise available, and it thus remains unclear whether it would be an exponential at all.…”

Section: E Degree Distributionsmentioning

confidence: 98%

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Lange

Sippel

Rosso

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Horizontal Visibility Graphs (HVGs) are a recently developed method to construct networks from time series. The values of the time series are considered as the nodes of the network and are linked to each other if there is no larger value between them, such as they can "see" each other. The network properties reflect the nonlinear dynamics of the time series. For some classes of stochastic processes and for periodic time series, analytical results can be obtained for network-derived quantities such as the degree distribution, the local clustering coefficient distribution, the mean path length, and others. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. Here, we investigate the sensitivity of the HVG methodology to properties and pre-processing of real-world data, i.e., time series length, the presence of ties, and deseasonalization, using a set of around 150 runoff time series from managed rivers at daily resolution from Brazil with an average length of 65 years. We show that an application of HVGs on real-world time series requires a careful consideration of data pre-processing steps and analysis methodology before robust results and interpretations can be obtained. For example, one recent analysis of the degree distribution of runoff records reported pronounced sub-exponential "long-tailed" behavior of North American rivers, whereas another study of South American rivers showed hyper-exponential "short-tailed" behavior resembling correlated noise. We demonstrate, using the dataset of Brazilian rivers, that these apparently contradictory results can be reconciled by minor differences in data-preprocessing (here: small differences in subtracting the seasonal cycle). Hence, data-preprocessing that is conventional in hydrology ("deseasonalization") changes long-term correlations and the overall runoff dynamics substantially, and we present empirical consequences and extensive simulations to investigate these issues from a HVG methodological perspective. After carefully accounting for these methodological aspects, the HVG analysis reveals that the river runoff dataset shows indeed complex behavior that appears to stem from a superposition of short-term correlated noise and "long-tailed behaviour," i.e., highly connected nodes. Moreover, the construction of a dam along a river tends to increase short-term correlations in runoff series. In summary, the present study illustrates the (often substantial) effects of methodological and data-preprocessing choices for the interpretation of river runoff dynamics in the HVG framework and its general applicability for real-world time series.

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Section: E Degree Distributionsmentioning

confidence: 98%

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Lange

Sippel

Rosso

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

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“…In the past decade many methods in a different application domains have been proposed to make this distinction, the most recent are reported in Skiadas and Skiadas (2016), Ravetti et al (2014), Rohde (2008), Gao et al (2006), and Rosso et al (2007). …”

Section: Detecting Chaos In B Subtilis Sporulation Network Dynamicsmentioning

confidence: 99%

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics

Lecca¹,

Mura²,

Re³

et al. 2016

Front. Microbiol.

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Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

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“…The topology of a graph is characterized by the degree distribution, p(k), that is the probability that a node has k links. Thus, the entropy of the degree distribution, S HV G = p k log(p k ) (in the following, referred to as HVG entropy), is another measure of the complexity of the time series {x i } [18]. An appropriate normalization of the HVG entropy is that of the Gaussian white noise, which rapidly converges to stable values for increasing time series lengths (percentage variations for times series with N = 10 5 and N = 5 × 10 5 data points are 10 4 and 10 5 ; in contrasts, the normalization through log(N) results in decreasing entropy values as N increases [18]).…”

Section: The Time-series Analysismentioning

confidence: 99%

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

et al. 2016

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Fibre lasers have been shown to manifest a laminar-to-turbulent transition when increasing its pump power. In order to study the dynamical complexity of this transition we use advanced statistical tools of time-series analysis. We apply ordinal analysis and the horizontal visibility graph to the experimentally measured laser output intensity. This reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods allow us to unveil coherent structures with well defined time-scales and strong correlations both, in the timing of the laser pulses and in their peak intensities.

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Distinguishing Noise from Chaos: Objective versus Subjective Criteria Using Horizontal Visibility Graph

Cited by 82 publications

References 81 publications

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

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