  We propose a stochastic model of web user behaviors in online social systems,
and study the influence of attraction kernel on statistical property of user or
item occurrence. Combining the different growth patterns of new entities and
attraction patterns of old ones, different heavy-tailed distributions for
popularity and activity which have been observed in real life, can be obtained.
  From a broader perspective, we explore the underlying principle governing the
statistical feature of individual popularity and activity in online social
systems and point out the potential simple mechanism underlying the complex
dynamics of the systems.
