Opinion dynamics on directed small-world networks

TL;DR

This paper studies how self-affirmation and long-range interactions influence opinion formation on directed small-world networks, revealing phase transitions between consensus and disordered states.

Contribution

It introduces a model analyzing the combined effects of self-affirmation and network topology on opinion dynamics, highlighting different phase transition behaviors.

Findings

System exhibits non-equilibrium phase transition from consensus to disorder.

Transition type depends on long-range interaction density and self-affirmation strength.

High self-affirmation and dense interactions lead to no phase transition.

Abstract

In this paper, we investigate the self-affirmation effect on formation of public opinion in a directed small-world social network. The system presents a non-equilibrium phase transition from a consensus state to a disordered state with coexistence of opinions. The dynamical behaviors are very sensitive to the density of long-range interactions and the strength of self-affirmation. When the long-range interactions are sparse and individual generally does not insist on his/her opinion, the system will display a continuous phase transition, in the opposite case with high self-affirmation strength and dense long-range interactions, the system does not display a phase transition. Between those two extreme cases, the system undergoes a discontinuous phase transition.