Polarization of Multi-agent Gradient Flows Over Manifolds With Application to Opinion Dynamics

• 成果类型: Article
• 署名作者: Mi, La; Goncalves, Jorge; Markdahl, Johan
• 署名单位: University of Luxembourg; University of Cambridge
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3281980
• 发表日期: 2024
• 页码: 1288-1295
• 关键词: Agents and autonomous systems; network analysis and control; Nonlinear systems; polarization; stability of nonlinear (NL) systems

摘要

Multi-agent systems are known to exhibit stable emergent behaviors, including polarization, over R-n or highly symmetric nonlinear spaces. In this article, we eschew linearity and symmetry of the underlying spaces, and study the stability of polarized equilibria of multi-agent gradient flows evolving on general hypermanifolds. The agents attract or repel each other according to the partition of the communication graph that is connected but otherwise arbitrary. The manifolds are outfitted with geometric features styled dimples and pimples that characterize the absence of flatness. The signs of interagent couplings together with these geometric features give rise to stable polarization under various sufficient conditions. We propose tangible interpretation of the system in the context of opinion dynamics, and highlight throughout the text its versatility in modeling diverse aspects of the polarization phenomenon.