Fractal Analysis on Human Behaviors Dynamics

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.