A fixed point analysis of multiple information coevolution spreading on social networks.

As a large, multiplicative, and diverse system, online social network allows people to study, share, collaborate, and spread rumors, which leads to the formation of online multiple information coevolution spreading networks (MICSNs). On these sophisticated networks, information spreads in an interactive way, and this coevolution spreading may cause emergence. When emergence is out of control, it may lead to some negative effects. So how to forecast emergence by stability monitoring is one of the most important bases for related issues. Most existing studies have focused only on separate macro-level factors or on the spreading principles of only one piece of information at a time. However, the coevolutionary spreading of several pieces of information leads to far greater monitoring and prediction difficulties. In this paper, by integrating mutual influencing factors (e.g., personal preferences, information acceptance, save endowment, and connection strength) a well-established two-stage feedback member model is proposed to reflect real situations of MICSNs. Based on this model, as an indicator of their states, a fixed point of MICSNs, stored information vector sum, is formally deducted. And the validity is verified by well-designed simulations, which compare value fluctuations of this fixed point with those of the irrational population and information existence time. Furthermore, the proposed fixed point can be used to monitor the states of MICSNs, alert administrators to potentially negative events, and provide theoretical guidance for public opinion analysis.