Mode interactions and fluctuations in the Kuramoto model of coupled oscillators

Phase dynamical models of weakly coupled oscillators have been the subject of extensive theoretical study since the early research of Winfree and Kuramoto established their relevance for understanding collective synchronization of oscillator populations.[1, 10] In this paper, we relax some of the key assumptions of the widely-used Kuramoto model of coupled phase oscillators. The coupling function of the model in its original form limits the types of entrained states; we allow for an arbitrary coupling function and look at the complexities that arise when two modes become critical simultaneously. In addition, we explore finite size effects to determine the size of the fluctuations of the order parameter for the case of subcritical coupling.