标题： 复杂系统中双标度定律的出现 显示英文标题

标题： Emergence of double scaling law in complex system

摘要： 我们引入一个随机模型来解释双幂律分布，该分布在其上尾和下尾表现出两种不同的帕累托行为，并广泛存在于社会和经济系统中。 该模型结合了适应性考虑和噪声波动。 我们发现，如果变量的数量（例如复杂网络中节点的度数或人们的收入）呈指数增长，正态分布的适应性与呈指数增长的变量共同导致双幂律分布的出现。 波动不会定性地改变结果，但会对第二部分的标度指数做出贡献。 中国航空网络的演化被用作一个例子，以显示与我们的随机模型的良好一致性。 显示英文摘要

摘要： 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.