Opinion Dynamics With Antagonistic Relationship and Multiple Interdependent Topics

Abstract

In this paper, the opinion dynamics model with antagonistic (competitive) relationship, multiple interdependent topics and the stubborn individuals is investigated. Different from the classical Friedkin-Johnsen (FJ) model, in our model, antagonistic and cooperative relationships are considered simultaneously. Furthermore, multiple logically interdependent topics are discussed in our model where the logical interdependence between the different topics is captured by a logic matrix. For structurally balanced and unbalanced network topologies, we rigorously examine the stability and convergence of our proposed model. A few conditions of stability and convergence are obtained. These conditions completely depend on network topology, stubborn coefficient and the logic matrix. They fully show that these factors jointly affect the evolution of opinions. Finally, a few numerical simulations are provided to illustrate our obtained results.