Rumor Propagation With Self‐Awareness and Event‐Triggered Intermittent Control Strategy

ABSTRACT The emergence of rumors indisputably poses significant harm to society and individuals. So as to deeply study the mechanism of rumor propagation, this article comprehensively considers various factors such as individual self‐awareness, saturation spread rate, and time delay to meticulously formulate a dynamic system of rumor dissemination in online social networks. Initially, the basic reproduction number is derived utilizing the next‐generation matrix method, thereby validating the existence of rumor equilibrium points. Secondly, leveraging the Jacobian matrix method and Lyapunov stability theory, we rigorously prove the local stability and global asymptotic stability of both the rumor‐free equilibrium and the rumor equilibrium. Subsequently, we also delve into the existence conditions of Hopf bifurcation. In addition, a new event‐triggered intermittent control strategy is proposed to suppress the spread of rumors. Finally, numerical simulations are proved to validate the effectiveness of the theoretical results.