Emergence of double scaling law in complex systems

¹ School of Information Science and Technology, East China Normal University - Shanghai 200241, China
² Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University Shanghai 200241, China
³ Shanghai Institute of Applied Physics, Chinese Academy of Sciences - Shanghai 201800, China
⁴ Graduate School of the Chinese Academy of Sciences - Beijing 100080, China

^a ddan@ee.ecnu.edu.cn

Received: 15 December 2010
Accepted: 14 March 2011

Abstract

We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. the degree of nodes in complex networks or people's incomes) grows exponentially, the normal distributed fitness coupled with exponentially increasing variable is responsible for the emergence of the double power-law distribution. Fluctuations do not change the result qualitatively but contribute to the second-part scaling exponent. The evolution of the Chinese airline network is taken as an example to show a nice agreement with our stochastic model.