2009/03/27 by Hayato Chiba, Diego Pazó
Physics and Astronomy · #nlin.AO
paper · pdf · doi:10.1016/j.physd.2009.03.005
to appear in Physica D
arxiv created 2009/03/27 · arxiv updated 2015/05/13
When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2]+1 (N is the population size). A global phase shift invariance allows to reduce the model to N-1 dimensions using the phase differences, and doing so the invariant torus becomes [N/2]-dimensional. By means of perturbative calculations based on the renormalization group technique, we show that this torus is asymptotically stable at small coupling if N is odd. If N is even the torus can be stable or unstable depending on the natural frequencies, and both possibilities persist in the small coupling limit.