Nonlinear Opinion Dynamics using Disagreement Laplacian Flows in Antagonistic Networks

Abstract

Coopetitive (competitive and cooperative) interactions in multi-agent systems lead to consensus, polarisation or clustering of opinions depending on the network structures. This paper studies the evolution of opinions for heteroge-neous networks with antagonistic interactions exploring the convergence properties of the opinions on the underlined network structures. We propose the opinion dynamics is in the form of a nonlinear disagreement Laplacian flow. We present conditions on structurally balanced digraphs which lead to opinion polarisation (or modulus consensus) in nonlinear framework. Finally, we analyse the evolution of opinions in structurally unbalanced networks that are weakly connected and have spanning tree(s). The results for all the cases are demonstrated through simulation results.