Dynamical Behaviors of a Delayed Fractional-Order Rumor Propagation Model with Saturated Control Terms

Restricted by the inherent limitations of integer-order rumor propagation models, the application of fractional-order derivatives in rumor-spreading dynamics has attracted increasing research attention. In this paper, a delayed fractional-order ISR rumor propagation model with saturated control terms is established. The stability of system equilibrium points and the Hopf bifurcation induced by time delay are analyzed. Numerical simulations reveal that the critical bifurcation delay increases monotonically with the fractional order, which indicates that the stability region of the system expands as the fractional order increases. Moreover, the introduction of government saturated intervention can effectively suppress rumor diffusion. The obtained conclusions can provide theoretical support for public opinion prevention and control.