Non-linear consensus dynamics on temporal hypergraphs with random noisy higher-order interactions

Abstract Complex networks encoding the topological architecture of real-world complex systems have recently been undergoing a fundamental transition beyond pairwise interactions described by dyadic connections among nodes. Higher-order structures such as hypergraphs and simplicial complexes utilized to model group for varied networked from brain, society, biological physical systems. In this article, we investigate consensus dynamics over temporal featuring non-linear modulating functions, time-dependent topology random perturbations. Based upon analytical tools in matrix, hypergraph, stochastic process real analysis, establish sufficient conditions all nodes network reach sense almost sure convergence $\mathscr{L}^2$ convergence. The rate moments equilibrium determined. Our results offer theoretical foundation recent series numerical studies observations multi-body dynamical