Noise-Based Control of Opinion Dynamics

Designing feasible control strategies for opinion dynamics in complex social systems has never been an easy task. It requires a control protocol, which 1) is not enforced on all individuals in the society, and 2) does not exclusively rely on specific opinion values shared by the social system. Thanks to the recent studies on noise-induced consensus in opinion dynamics, the noise-based intervention strategy has emerged as the only one meeting both of the above requirements, yet its underlying general theory is still lacking. In this article, we perform rigorous theoretical analysis and simulations of a noise-based control strategy for opinion formation, in which only a fraction of individuals is affected by randomly generated noise. We develop a new approach to prove the existence of a feasible noise protocol when it is difficult to be explicitly constructed and prove that irrespective of the number of noise-driven individuals, including the case of only one single noise-affected individual, the system can be controlled to achieve quasi-consensus in finite time, and the critical noise strength can be obtained. Our results highlight the efficiency of noise-driven mechanisms for the control of complex social dynamics.