Consensus analysis of a two-step communication opinion dynamics model with group pressure and self-confidence

TL;DR

This paper studies a new opinion dynamics model incorporating group pressure and self-confidence, accounting for two-step social influence, and proves conditions for achieving consensus with exact consensus values.

Contribution

It introduces a two-step communication model considering friends of friends influence, extending existing models and providing analytical consensus conditions and values.

Findings

Consensus can be achieved under the model.

Exact consensus values are derived for different group pressure cases.

Simulation confirms theoretical results.

Abstract

This paper considers the consensus problem of a novel opinion dynamics model with group pressure and self-confidence. Different with the most existing paper, the influence of friends of friends in a social network is taken into account, which is modeled to be two-step communication. Based on this consideration, the neighbors of agents are classified into direct neighbors and indirect neighbors. Accordingly, the communication between agents and their neighbors is classified into one-step communication and two-step communication. By applying matrix analytic theory and graph theory, it is shown that the opinion consensus can be achieved. Moreover, the exactly consensus value of the opinion is obtained for three cases of the group pressure. Finally, simulation examples are provided to demonstrate the validity of the conclusions drawn in the paper.