Higher order interactions in Kuramoto oscillators with inertia

Abstract

How higher-order interactions influence the dynamics of second order phase oscillators? We address this question using three coupled Kuramoto phase oscillators with inertia under both pairwise and higher order interactions, finding collective states, which are absent for pair-wise interactions. Chimera states appear in an expanded parameter region of the 3-node network by comparison to the network's response in the absence of the higher-order interactions. %That attempt enables us to understand the emergence of chimera states. This small network of three nodes is investigated for different sets of phase lags and over a range of negative to positive coupling strength of pairwise as well as higher order or group interactions. It demonstrates how important are the choices of the phase lag and the sign of the coupling for the emergent dynamics of the system.