Leader-Follower Opinion Dynamics of Signed Social Networks With Asynchronous Trust/Distrust Level Evolution

Trust and distrust are common in the opinion interactions among agents in signed social networks. To explain the gradual evolution of the trust/distrust level between agents due to opinion difference, this paper proposes a new opinion dynamic model with asynchronous evolution of edge weights. In the model, the trust/distrust level between agents is portrayed as a nonlinear weight function of their opinion difference, and each agent only interacts with the neighbors at the times determined by its own will. In the presence of a stubborn leader with a firm stand, a comprehensive theoretical analysis for opinion consensus and opinion polarization is performed by using the related properties of sub-stochastic and super-stochastic matrices. Moreover, the opinion dynamics over an arbitrary underlying network with multiple non-stubborn leaders is further explored. Finally, some numerical simulations are provided to illustrate the theoretical results.