The Modified Form of the Gutenberg-Richter Law ‎in ‎Solar ‎Flare ‎Complex ‎Network‎ : ‎Approach of Genetic Algorithm on the Thresholded Power-Law Behavior

Abstract

The hybrid model approach is adopted to construct the solar flare complex network. The modified form of Gutenberg-Richter law is obtained as the frequency-magnitude distribution of the empirical data. The frequency-magnitude distributions of positive-definite data are sometimes observed to follow a power-law over several orders of size. There are reasons to the deviation of the frequency-magnitude distribution from an ideal power distribution. Among many alternative forms of the power-law function, we found that the threshold power-law is well fitted with solar empirical data at small values. A statistical method based on optimization of the ‎$‎‎chi‎‎^{2}‎$-test by application of the genetic algorithm have been developed.‎Here, the analytical details of a method based on genetic algorithm is presented to calculate the parameters of the frequency-Magnitud‎‏e distribution of the empirical data sets. This method estimates the best parameters of the threshold power-law function as the frequency-magnitude distribution of the empirical data, as well.

Keywords

• ‎ solar flare‎
• ‎ complex network‎
• the gutenberg-richter law
• genetic algorithm
• frequency-magnitude distribution‎
• thresholded power-law ‎ behavior&lrm