Evolution analysis of two-layer time-varying trust Hegselmann-Krause models with opinion leaders

As a typical state-dependent model which considers psychological factors, bounded confidence model is becoming a popular tool in opinion evolution analysis. In this paper, a novel two-layer time-varying trust Hegselmann-Krause model (two-layer THK model) is proposed by describing the “Similarity Effect” in psychology. The two-layer THK model consists of leader-layer and follower-layer. Leaders in leader-layer are agents with reputation and more power to influence others. Followers in follower-layer are agents with sensitivity, which can change their trust to others according to opinion differences. We analyze the convergence of the proposed model and simulate phenomena of opinion polarization in reality. Simulations reveal the following facts: Reputation of leaders does not have obvious effects on opinion polarization. High sensitivity and proper confidence radius are promotive to opinion polarization.