4.7 Article

Existence of hysteresis in the Kuramoto model with bimodal frequency distributions

Journal

PHYSICAL REVIEW E
Volume 80, Issue 4, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.046215

Keywords

hysteresis; modal analysis; phase transformations; synchronisation

Funding

  1. CSIC under the Junta de Ampliacion de Estudios Programme (JAE-Doc)
  2. Ministerio de Educacion y Ciencia (Spain) [FIS2006-12253-C06-04]
  3. Centre de Recerca Matematica (CRM), 08193 Bellaterra, Barcelona, Spain

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We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

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