On computing the critical coupling coefficient for\ud the Kuramoto model on a complete bipartite\ud graph

摘要

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