Nonlinear Opinion Dynamics in Systems with Leadership Effect

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.