Emergence of double scaling law in complex system

TL;DR

This paper presents a stochastic model explaining the emergence of double power-law distributions in social and economic systems, highlighting the roles of fitness, noise, and exponential growth, with empirical validation on the Chinese airline network.

Contribution

It introduces a novel stochastic model that accounts for double power-law distributions through fitness and noise, supported by empirical data from the Chinese airline network.

Findings

Double power-law distributions arise from exponential growth and fitness.

Fluctuations influence the second scaling exponent but do not alter the overall distribution.

Empirical data from Chinese airline network aligns with the model's predictions.

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, 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 Chinese airline network is taken as an example to show a nice agreement with our stochastic model.