Opinion Dynamics on the Sphere for Stable Consensus and Stable Bipartite Dissensus

Abstract

In this paper, we develop a multi-agent model for opinion dynamics that offers rich behaviors of opinion formations. The states of the model are the opinions of the agents which are designed to evolve on a unit-sphere. The model is novel in that the input to the system is designed based on a correlation matrix of the opinions of neighboring agents. Interestingly, the model demonstrates both stable consensus as well as stable bipartite dissensus behaviors using an unsigned communication graph. This is different than existing results where stable dissensus can only be achieved via a signed graph. We present various stability results about the different equilibrium configurations. Additionally, we provide simulation results for a 2-dimensional system demonstrating the different resulting behaviors of the system.