Symmetry-breaking higher-order interactions in coupled phase oscillators

Abstract

This paper investigates the route to synchronization in an extension of the Kuramoto model, which incorporates higher order interactions and do not preserve rotational symmetry, resulting in interesting dynamical scenarios. Using the standard Kuramoto order parameter and the Ott–Antonsen ansatz, the transition points corresponding to different dynamical characteristics are identified and the extent of synchrony is quantified. These results indicate that the system exclusively undergoes explosive transitions and dynamical states are dependent on the mean natural frequency. Interestingly, for a certain range of parameter values, an unsteady yet partially synchronized state characterized by an oscillatory order parameter is observed. The analytical results are shown to agree well with the numerical simulations.