Complex Network for Solar Active Regions

Abstract

Here, we developed a complex network of solar active regions (ARs) to study various local and global properties of the network. The values of the Hurst exponent (0.8 − 0.9) were evaluated by both the detrended fluctuation analysis and the rescaled range analysis applied on the time series of the AR numbers. The findings suggest that ARs can be considered as a system of self-organized criticality.We constructed a growing network based on locations, occurrence times, and the lifetimes of 4,227ARs recorded from 1 January 1999 to 14 April 2017. The behaviour of the clustering coefficient shows that the ARs network is not a random network. The logarithmic behaviour of the length scale has the characteristics of a so-called "small-world network". It is found that the probability distribution of the node degrees for undirected networks follows the power-law with exponents of about 3.7 to 4.2.This indicates the scale-free nature of the ARs network. The scale-free and small-world properties of the ARs network confirm that the system of ARs forms a system of self-organized criticality. Our results show that the occurrence probability of flares (classified by GOES class C > 5, M, and X flares) in the position of the ARs network hubs take values greater than that obtained for other nodes.Corresponding author: Hossein Safari safari@znu.ac.ir Daei, Safari, and Dadashi

Research on the joint fluctuation laws between locational marginal price and renewables based on complex networks: A case study in Independent System Operator New England

“…In some literature, similar cases are fitted to power‐law distribution to reveal the scale‐free feature of the networks. But the fitting effect is sometimes not good enough . The fitting result in this paper indicates that the degree distribution of the network is deviated from a pure power‐law and conformed to an exponential.…”

Evidence of Self-Organised Criticality in Time Series by the Horizontal Visibility Graph Approach

“…Whilst, the maximum eigenvalues of Bak and Manna sandpile models are in the range of 5.5 − 6.3. The average clustering coefficients 6,7,10,55,56 of mentioned TS are also presented in Figure 5. Likewise the maximum eigenvalues, the average clustering coefficients of both sand-pile models are distinguishable from the random and chaos processes.…”

“…The problem becomes more intricate when there isn't a comprehensive description of the subject system or the phenomenon encompasses a wide range of fields. Complex systems seem to confront with both, because on the one hand there is no all-inclusive interpretation of these systems [2][3][4] , and on the other hand they include everything from brain structure to insect colonies, price fluctuations in financial markets, condensate matter, Internet, Plasma and Solar physics, and even all human societies 3,[5][6][7][8][9][10] . Given the breadth and intricacy mentioned, classifying complex systems is an outstanding issue that has attracted vast research interests [11][12][13][14] .…”

Principle of Minimum Energy in Magnetic Reconnection in a Self-organized Critical Model for Solar Flares

“…Empirical evidence implies the ubiquitous presence of power-law distributions in various fields. This has inspired wide research in physics, geophysics, biology, social sciences, etc., such as studies on self-organized systems (Bak et al 1987;Newman 2005;Clauset et al 2009;Alipour & Safari 2015), fractal geometry (Mandelbrot 1975), and the scale-free and small-world complex networks (Barabási & Bonabeau 2003;Abe & Suzuki 2006;Daei et al 2017;Gheibi et al 2017).…”