Weblog patterns and human dynamics with decreasing interest

Abstract

In order to describe the phenomenon that people’s interest in doing something always keep high in the beginning while gradually decreases until reaching the balance, a model which describes the attenuation of interest is proposed to reflect the fact that people’s interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, which is a power law with an exponential cutoff. After that, we collect blogs in ScienceNet.cn and carry on empirical study on the interarrival time distribution. The empirical results agree well with the theoretical analysis, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model by providing an evidence for a new class of phenomena in human dynamics. It can be concluded that besides power-law distributions, there are other distributions in human dynamics. These findings demonstrate the variety of human behavior dynamics.