A Unified Framework for Convergence Analysis in Social Networks

This paper proposes a unified framework for the stability analysis of discrete-time nonlinear systems from social networks, including the Friedkin-Johnsen opinion model, two opinion dynamics models in the study of social power, and a general nonlinear polar opinion model. Three novel convergence results are proposed to treat various conditions based on LaSalle invariance principle. Several applications are provided to illustrate the power of the proposed framework.