Verwoerd, Mark and Mason, Oliver
On computing the critical coupling coefficient for
the Kuramoto model on a complete bipartite
SIAM Journal on Applied Dynamical Systems, 8 (1).
We extend recent results  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.
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