A stochastic rumor spreading model with event-triggered discontinuous feedback control in multilingual online networks

Benefiting from the development of Internet technology, online social networks with multilingual communication function are in a booming stage, greatly contributing to the convenience, extensiveness and diversity of information exchange. To explore the rumor diffusion mechanism and efficient control strategies in multilingual online environments, a novel stochastic rumor-spreading model with the generalized nonlinear diffusion form is proposed. Firstly, we strictly prove the positive and existence uniqueness of the model solution to ensure that it corresponds to the realistic meaning. Then, the asymptotic behavior around the rumor-free equilibrium is acquired by using graph theorey and stochastic stability theory. Besides, we obtain conditions for the stationary distribution of stochastic rumor-spreading model based on the Kasminskii's theory. Moreover, an event-triggered discontinuous feedback (ETDF) control strategy that can be applied to online networks is proposed, which initiates control only when an alert threshold is exceeded and updates the control intensity when an event-triggered condition is reached. Finally, numerical simulations verify the correctness of the theoretical results, and an actual multilingual Internet rumor case shows the applicability of the model.