人类行为动力学的分形分析
Fractal Analysis on Human Behaviors Dynamics
摘要：
近年来，人体动力学的研究引起了许多领域的兴趣。本文从图书馆借阅量时间序列的角度研究了人类行为的分形特征。通过重标极差分析计算出的Hurst指数和非周期环的长度表明，人类行为时间序列是具有长程相关性的分形序列。然后利用可见图算法将时间序列转化为复杂网络。网络的无标度性、小世界效应和层次结构等拓扑特性表明，人们在一定时间内，特别是在重要的日子里，重复行为的数量与行为的发生有着密切的关系。最后，用盒计数法验证了所得到的网络是非分形和自相似的。我们的工作揭示了人类集体重复行为的内在规律性。
英文摘要：
The study of human dynamics has attracted much interest from many fields recently. In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The Hurst exponents and length of non-periodic cycles calculated through Rescaled Range Analysis indicate that the time series of human behaviors is fractal with long-range correlation. Then the time series are converted to complex networks by visibility graph algorithm. The topological properties of the networks, such as scale-free property, small-world effect and hierarchical structure imply that close relationships exist between the amounts of repetitious actions performed by people during certain periods of time, especially for some important days. Finally, the networks obtained are verified to be not fractal and self-similar using box-counting method. Our work implies the intrinsic regularity shown in human collective repetitious behaviors.
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