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Author: Small, M. Ă—

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    Advances in Time Series Analysis and Its Applications
    (New York, NY : Hindawi Publishing Corporation, 2016) Gao, Z.-K.; Small, M.; Donner, R.; Meng, D.; Ghaffari, H.O.
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    Complex network approach to characterize the statistical features of the sunspot series
    (Bristol : Institute of Physics Publishing, 2014) Zou, Y.; Small, M.; Liu, Z.; Kurths, J.
    Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse- transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network that span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15-1000 days by a power-law regime with scaling exponent Îł = 2.04 of the occurrence time of two subsequent strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models.
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    Long-term changes in the north-south asymmetry of solar activity: A nonlinear dynamics characterization using visibility graphs
    (Göttingen : Copernicus GmbH, 2014) Zou, Y.; Donner, R.V.; Marwan, N.; Small, M.; Kurths, J.
    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.