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

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 modelling analysis dynamical behaviours. Here, we study simple three-body consensus model, which favourably incorporates higher-order network interactions, dimensional states, the group reinforcement effect homophily principle. The model features asymmetric roles acting using modulating functions. We analytically establish sufficient conditions for nonlinear conservation states with both discrete-time continuous-time dynamics. show that interactions encoded edges give rise to gravity-like Heaviside-like Furthermore, illustrate our theoretical results numerical simulations examine system convergence time through depreciation process.