Multifractal analysis of solar flare indices and their horizontal visibility graphs

Yu, Zu-Guo; Anh, Vo; Eastes, R.; Wang, Danling

doi:10.5194/npg-19-657-2012

Cited by 22 publications

(22 citation statements)

References 65 publications

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“…Nevertheless, similar to normal VGs, HVGs have been successfully applied to studying time series from various fields of sciences. Within the scope of the present manuscript, we particularly highlight the recent paper by Yu et al (2012), who studied the multifractal properties of a solar flare index in terms of HVG characteristics.…”

Section: Horizontal Visibility Graphsmentioning

confidence: 99%

“…In recent years, a variety of approaches have been introduced by various authors (see Donner et al, 2011 for a review), with recurrence networks Donner et al, 2010a) and visibility graphs (Lacasa et al, 2008) as probably the two most prominent and widely applied concepts. Specifically, some variants of visibility graph analysis have been used recently to study the statistical properties of different solar activity indicators (Yu et al, 2012;Zou et al, 2014b). However, these analyses have been restricted to univariate time series so far, not allowing for an explicit study of interhemispheric asymmetry properties.…”

Section: Introductionmentioning

confidence: 99%

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Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Zou

Donner

Marwan

et al. 2014

Nonlin. Processes Geophys.

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Abstract. Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.

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Section: Horizontal Visibility Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Zou

Donner

Marwan

et al. 2014

Nonlin. Processes Geophys.

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“…[e.g., Schertzer and Lovejoy, 1987;Schmitt et al, 1992;Tessier et al, 1993Tessier et al, , 1996Olsson and Niemzcynowicz, 1996;Harris et al, 1996;Lovejoy et al, 1996Lovejoy et al, , 2008Deidda, 2000;Lilley et al, 2006;Kantelhardt et al, 2006;Veneziano et al, 2006;Venugopal et al, 2006;Lovejoy and Schertzer, 2006, 2010a, 2010bGarcia-Marin et al, 2008;Serinaldi, 2010;. In particular, Lui [2002] Anh et al [2007Anh et al [ , 2008 and Yu et al [2010Yu et al [ , 2012 used MFA and fractional stochastic differential equations to study the AE and geomagnetic field data. This paper aims to identify significant similarities in the scaling properties of geomagnetic and solar indices.…”

Section: Journal Of Geophysical Research: Space Physicsmentioning

confidence: 99%

“…Yu et al [2012] proposed a simple method to estimate the parameters H, C 1 , and . In this paper, we adopt the method in Yu et al [2012] …”

Section: 1002/2014ja019893mentioning

confidence: 99%

Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

Anh

Eastes

2014

JGR Space Physics

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This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (a p and AE), two solar indices (solar X-rays X l and solar flux F10.7), and two inner heliospheric indices (ion density Ni and flow speed Vs) over the period 1995-2001 by the universal multifractal approach and the traditional multifractal analysis. We found that the universal multifractal model (UMM) provides a good fit to the empirical K(q) and (q) curves of these time series. The estimated values of the Lévy index in the UMM indicate that multifractality exists in the time series for a p , AE, X l , and Ni, while those for F10.7 and Vs are monofractal.The estimated values of the nonconservation parameter H of this model confirm that these time series are conservative which indicate that the mean value of the process is constant for varying resolution. Additionally, the multifractal K(q) and (q) curves, and the estimated values of the sparseness parameter C 1 of the UMM indicate that there are three pairs of indices displaying similar scaling properties, namely a p and X l , AE and Ni, and F10.7 and Vs. The similarity in the scaling properties of pairs (a p , X l ) and (AE, Ni) suggests that a p and X l , AE and Ni are better correlated-in terms of scaling-than previous thought, respectively. But our results still cannot be used to advance forecasting of a p and AE by X l and Ni, respectively, due to some reasons.

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“…The HVG has been used to study the daily solar X-ray brightness data [25] and protein molecular dynamics [26] by our group.…”

Section: Introductionmentioning

confidence: 99%

Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

Yu¹,

Zhang²,

Huang³

et al. 2016

J. Stat. Mech.

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Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace spectrum of the horizontal visibility graphs (HVGs) constructed from fractional Brownian motions. We aim to identify via simulation and curve fitting the form of these properties in terms of the Hurst index H. First, we use the sandbox algorithm to study the multifractality of these HVGs. It is found that multifractality exists in these HVGs. We find that the average fractal dimension D (0) Then, we calculate the spectrum and energy for the general Laplacian operator and normalized Laplacian operator of these HVGs. We find that, for the general Laplacian operator, the average logarithm of second-smallest eigenvalue ln(u 2 ) , the average logarithm of third-smallest eigenvalue ln(u 3 ) , and the average logarithm of maximum eigenvalue ln(u n ) of these HVGs are approximately linear functions of H; while the average Laplacian energy E nL is approximately a quadratic polynomial function of H. For the normalized Laplacian operator, ln(u 2 ) and ln(u 3 ) of these HVGs approximately satisfy linear functions of H; while ln(u n ) and E nL are approximately a 4th and cubic polynomial function of H respectively.

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Multifractal analysis of solar flare indices and their horizontal visibility graphs

Cited by 22 publications

References 65 publications

Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

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