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The stochastic dynamical theory for the complex systems with power-law distributions
Du Jiulin * #
Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
*Correspondence author
#Submitted by
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Funding: National Natural Science Foundation（No.11175128）, Higher School Specilized Research Fund of Doctoral Programm（No.20110032110058）
Opened online:26 November 2015
Accepted by: none
Citation: Du Jiulin.The stochastic dynamical theory for the complex systems with power-law distributions[OL]. [26 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4661711
 
 
The stochastic dynamical theory for the systems with power-law distributions has been discussed by means of using the Langevin equations with inhomogeneous friction and noise and the corresponding Fokker-Planck equations. The power-law distributions and the generalized fluctuation-dissipation relation under which these distributions can be generated in a complex system away from equilibrium have been found. And simultaneously, the Klein-Kramers equation and the Smoluchowski equation have been generalized to the dynamical systems with the solutions of power-law distributions. The numerical analyses have shown the power-law distributions all excellently fitting with the solutions of the dynamics of the Langevin equations.
Keywords:Power-law distribution; Langevin equation; Fokker-Planck equation; Stochastic dynamics
 
 
 

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