2003/01/31 by Takashi Nishikawa, Frank C. Hoppensteadt
Mathematics · Physics and Astronomy · #math.DS #cond-mat.dis-nn #msc:34C15 #msc:37N25 #msc:37N20
published as SIAM J. Appl. Math., Vol. 63, No. 5, pp. 1615-1626 (2003) · 12 pages, 2 figures, to appear in SIAM J. Appl. Math., SIAM LaTeX Macros
arxiv created 2003/07/17 · arxiv updated 2009/11/30
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.