A system model of three-body interactions in complex networks: Consensus and conservation

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Abstract

Networked complex systems in a wide range of physics, biology and social sciences involve synergy among multiple agents beyond pairwise interactions. Higher-order mathematical structures such as hypergraphs have been increasingly popular in modelling and analysis of complex dynamical behaviors. Here, we study a simple three-body consensus model, which favorably incorporates higher-order network interactions, higher-order dimensional states, group reinforcement ef fect as well as social homophily principle. The model features asymmetric roles of acting agents using modulating functions. We analytically establish suf ficient conditions for nonlinear consensus and conservation of states for agents with both discrete-time and continuous-time dynamics. We show that higher-order interactions encoded in three-body edges give rise to consensus and conservation for systems with gravitylike and Heaviside-like modulating functions. Furthermore, we illustrate our theoretical results with numerical simulations and examine the system convergence time through a network depreciation process.
Original languageEnglish
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publication statusAccepted/In press - 7 Jan 2022

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