Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators |
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| Authors: | Luis L. Bonilla John C. Neu Renato Spigler |
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| Affiliation: | (1) Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, 35131 Padova, Italy;(2) Present address: Escuela Politecnica Superior, Universidad Carlos III de Madrid, 28913 Leganes (Madrid), Spain;(3) Department of Mathematics, University of California, 94720 Berkeley, California |
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| Abstract: | A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained. |
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| Keywords: | Nonlinear oscillators synchronization mean-field model bimodal distribution bifurcation nonlinear stability |
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