System of phase oscillators with diagonalizable interaction
arXiv:math/0301286
Abstract
We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators. We show that in the limit of N going to infinity, all solutions of such a system are incoherent with probability one for any strength of coupling, which implies that there is no sharp transition from incoherence to coherence as the coupling strength is increased, in striking contrast to Kuramoto's (special) oscillator system.
12 pages, 2 figures, to appear in SIAM J. Appl. Math., SIAM LaTeX Macros