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On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
 In Proceedings of the American Control Conference
, 2004
"... We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral gra ..."
Abstract

Cited by 58 (8 self)
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We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an alltoall connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.
To appear in SIAM J. Appl. Math. SYSTEM OF PHASE OSCILLATORS WITH DIAGONALIZABLE INTERACTION
, 2003
"... 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 → ∞, all solutions of such a system are incoherent with probability one for any strength of coupling, which impl ..."
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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 → ∞, 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. Key words. Network of phase oscillators, Kuramoto model AMS subject classifications. 34C15, 37N25, 37N20 1. Introduction. Synchronization
SYSTEM OF PHASE OSCILLATORS WITH DIAGONALIZABLE INTERACTION
, 2003
"... 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 → ∞, all solutions of such a system are incoherent with probability one for any strength of coupling, which imp ..."
Abstract
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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 → ∞, 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. Key words. Network of phase oscillators, Kuramoto model AMS subject classifications. 34C15, 37N25, 37N20 1. Introduction. Synchronization