Opinion Dynamics With Heterogeneous Multiple Interdependent Topics on the Signed Social Networks

This is the authors' abstract. We don't add key points for this paper.

In this article, based on the classical Degroot and Friedkin–Johnsen model, two opinion dynamics models with antagonistic relationship and multiple interdependent topics are proposed. The proposed models aim to characterize the evolution of individual opinions when individuals in a signed social network are able to discuss multiple interdependent topics simultaneously. Considering that different individuals may have different perceptions of the same thing, a set of heterogeneous logical matrices is used to represent the logical interdependence between different topics. In Model I with time-varying topologies, both the structurally balanced and unbalanced network topologies are investigated. Some sufficient conditions for the modulus consensus about topics are obtained in our study. About Model II with the stubborn individuals, we rigorously concentrate on its convergence and stability for the structurally balanced and unbalanced social networks. And some conditions on the convergence and stability are obtained. All the obtained conditions depend on the network topology and logical matrices and fully show how the network topology and logical matrices influence the evolution of opinions. Finally, two examples are used to verify our results.