Finite-Time Elimination of Disagreement of Opinion Dynamics via Covert Noise

Eliminating disagreement in a group is usually beneficial to the social stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we design a quite simple strategy that could resolve the opinion difference of the system in finite time and induce the opinions synchronized to a targeted value. To be specific, we intentionally introduce weak random noise to only one agent to affect its opinion in the evolution and also a leader agent with fixed opinion in a divisive group, then strictly prove that the disagreement is finally eliminated and the opinions get synchronized to the leader's opinion in finite time. Other than that, we calculate the finite stopping time when the opinions synchronously reach the objective opinion value, which could provide further guide for designing more efficient noise intervention strategy.