Mean Square Consensus under Coopetitive Social Networks with Communication Noise

This paper aims to investigate a stochastic Altafini model, in which individuals are disturbed by the communication noise. We use coopetitive networks to describe their affiliation of classes. Different from the general situations with noises, when the opinion values in the classes converge, the noise will decrease. We consider the communication noise, when the differences of opinion values are larger, the influences of noise are greater. When the opinion values are reaching to biparite consensus, the influences of noise are decreasing, such a design is more in line with the reality. By constructing the appropriate Lyapunov function, the conditions for the stochastic stability of the system are obtained. We get the conclusion of mean square biparite consensus. In addition, numerical simulation results can verify the theoretical results.