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Exploring S-shape curves and heterogeneity effects of rumor spreading in online collective actions.

Nowadays online collective actions are pervasive, such as the rumor spreading on the Internet. The observed curves take on the S-shape, and we focus on evolutionary dynamics for S- shape curves of online rumor spreading. For agents, key factors, such as internal aspects, external aspects, and hearing frequency jointly determine whether to spread it. Agent-based modeling is applied to capture micro-level mechanism of this S-shape curve. We have three findings: (a) Standard S-shape curves of spreading can be obtained if each agent has the zero threshold; (b) Under zero-mean thresholds, as heterogeneity (SD) grows from zero, S-shape curves with longer right tails can be obtained. Generally speaking, stronger heterogeneity comes up with a longer duration; and (c) Under positive mean thresholds, the spreading curve is two-staged, with a linear stage (first) and nonlinear stage (second), but not standard S-shape curves either. From homogeneity to heterogeneity, the spreading S-shaped curves have longer right tail as the heterogeneity grows. For the spreading duration, stronger heterogeneity usually brings a shorter duration. The effects of heterogeneity on spreading curves depend on different situations. Under both zero and positive-mean thresholds, heterogeneity leads to S-shape curves. Hence, heterogeneity enhances the spreading with thresholds, but it may postpone the spreading process with homogeneous thresholds.