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Bifurcations and singularities for coupled oscillators with inertia and frustration

Abstract : We prove that any non zero inertia, however small, is able to change the nature of the synchronization transition in Kuramoto-like models, either from continuous to discontinuous, or from discontinuous to continuous. This result is obtained through an unstable manifold expansion in the spirit of J.D. Crawford, which features singularities in the vicinity of the bifurcation. Far from being unwanted artifacts, these singularities actually control the qualitative behavior of the system. Our numerical tests fully support this picture.
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https://hal.inria.fr/hal-01336162
Contributor : Julien Barre <>
Submitted on : Wednesday, June 22, 2016 - 4:32:46 PM
Last modification on : Wednesday, October 14, 2020 - 4:24:35 AM

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Julien Barre, D Métivier. Bifurcations and singularities for coupled oscillators with inertia and frustration. 2016. ⟨hal-01336162⟩

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