Improved Finite Time in Eliminating Disagreement of Opinion Dynamics via Noise

Abstract

We aim to refine the estimation of the finite stopping time when the disagreement in an opinion group is eliminated by a simple but novel noise intervened strategy. It has been proved that, by using this noise intervened control strategy, the divisive opinions would get synchronized in finite time. Moreover, the finite stopping time when resolving the disagreement has been clarified. The estimation of the finite stopping time will effectively reveal which factors and how they determine the consequence of intervention. However, the upper bound for the estimation of the integrable stopping time when noise is oriented has been quite conservative. In this paper, we investigate the finite stopping time of eliminating the disagreement by completely oriented noise and a much more precise formula for the estimation of the finite stopping time is obtained finally via direct calculation.