Nonlinear Opinion Dynamics in Systems with Leadership Effect

TL;DR

This paper models opinion evolution in groups with a leader using a nonlinear dynamical system, analyzing stability and bifurcations to understand how leadership influences collective decision-making.

Contribution

It introduces a nonlinear opinion dynamics model incorporating leadership effects and provides bifurcation analysis for stability insights.

Findings

Bifurcation points identified in the model.

Leadership significantly affects opinion stability.

Nonlinear effects lead to complex opinion evolution patterns.

Abstract

Opinion dynamics of a group of individuals is the change in the members' opinions through mutual interaction with each other. The related literature contains works in which the dynamics is modeled as a continuous system, of which behavioral patterns are analyzed in regard to the parameters contained in the system. These models are constructed by the assumption that the individuals are independent. Besides, the decisions of the individuals are only affected by two forces: self-bias force and group influence force. In this work we consider a nonlinear dynamical system which models the evolution of the decision of a group under the existence of a leader. Bifurcation analysis of the system is performed to obtain stability results on the system.