Abstract

We extend recent results [50] on the existence of global phase-locked states (GPLS) in the Kuramoto model on a complete graph to the case of a complete bipartite graph. In particular, we prove that, for the Kuramoto model on a complete bipartite graph, the value of the critical coupling co- efficient can be determined by solving a system of two nonlinear equations that do not depend on the coupling coefficient. We show that the said system of equations can be solved using an efficient algorithm described in the paper.