Stable fixed points in the Kuramoto model

Details Stable fixed points in the Kuramoto model Stable fixed points in the Kuramoto model

2010-10-05

arxiv.org/abs/1010.0766v1

Physics

Mathematical Physics

10 pages

Scientific paper

We develop a necessary condition for the existence of stable fixed points for the general network Kuramoto model, and use it to show that for the complete network the homogeneous model has no non-zero stable fixed point solution. This result provides further evidence that in the homogeneous case the zero fixed point has an attractor set consisting of the entire space minus a set of measure zero, a conjecture of Verwoerd and Mason (2007).

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