Opinion Dynamics With Competitive Relationship and Switching Topologies

Guang He,Haoyue Ruan,Jing Liu,Yanlei Wu

doi:10.1109/access.2020.3047893

Guang He, Haoyue Ruan + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.3047893

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Abstract

In this paper, the discrete-time opinion dynamics model with competitive relationship and switching topologies is investigated. Different from the usual DeGroot model, competition between individuals and the switching topologies are considered in a social network. Furthermore, the structurally balanced and unbalanced network topologies are investigated simultaneously. It is shown that if all network topologies are structurally balanced and include a spanning tree, then there may appear polarization, neutralization or fluctuation. And we also find conditions under which the group is split into two clusters at most, specifically, opinions will reach polarization (bipartite consensus) or all individuals will remain neutrality (consensus). If there exist the structurally unbalanced network topologies in social networks, we obtain the condition in which all individuals will finally hold the neutral attitude on the discussed topic. Two examples are provided to illustrate the effectiveness of the obtained results.

Highlights

Recently, opinion dynamics, which has been studying the exchange and discussion of opinions between individuals which may occur in mediums and situations as varied as company boardrooms, elementary school classrooms and online social media, has drawn considerable attention from control theory, sociology, physics, economics, biology and so on [1]–[6]
The so-called opinion dynamics focuses on the basic problem of social networks: how individuals are influenced by the presence of others in a social group
If the network topology is strongly connected and aperiodic, DeGroot model always reaches an opinion consensus for the arbitrary initial opinions [12], i.e., all agents make an agreement about a topic

Summary

INTRODUCTION

Opinion dynamics, which has been studying the exchange and discussion of opinions between individuals which may occur in mediums and situations as varied as company boardrooms, elementary school classrooms and online social media, has drawn considerable attention from control theory, sociology, physics, economics, biology and so on [1]–[6]. The so-called opinion dynamics focuses on the basic problem of social networks: how individuals (agents) are influenced by the presence of others in a social group. If the network topology is strongly connected and aperiodic, DeGroot model always reaches an opinion consensus for the arbitrary initial opinions [12], i.e., all agents make an agreement about a topic. Different from the DeGroot model [12], in which each actor is completely open to interpersonal influence, the stubborn agents in the FJ model always consider their initial opinions for every iteration of opinions. In [7], the continuous-time DeGroot model on signed graphs was studied and a necessary and sufficient condition of polarization was obtained based on structurally balanced graphs. In the structurally unbalanced social networks, the relationship between individuals is more complicated, which makes it more difficult to analyze the model mathematically.

PRELIMINARIES

MATHEMATICAL PRELIMINARIES

NUMERICAL EXAMPLE

CONCLUSION