System of phase oscillators with diagonalizable interaction

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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

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Dynamical Systems, Disordered Systems and Neural Networks, 34C15, 37N25, 37N20

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http://salesiana.dossiersoluciones.com/handle/123456789/66346

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301286
 http://arxiv.org/abs/math/0301286
 SIAM J. Appl. Math., Vol. 63, No. 5, pp. 1615-1626 (2003)

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arXiv