Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Abstract Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based a recent formulation weighted simplicial complexes phases supported simplices any order k , we introduce linear and non-linear frustration terms independent orientation + 1 simplices, natural generalization Sakaguchi-Kuramoto to complexes. With increasingly complex complexes, study dynamics edge nonlinear highlight complexity emerging We discover various phenomena, partial loss synchronization subspaces aligned Hodge emergence phase re-locking regimes high frustration.