title: Existence of hysteresis in the Kuramoto model with bimodal frequency distributions.
abstract: 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.
authors.affiliation: Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain.
authors.forename: Diego
authors.initials: D
authors.lastname: Pazó
authors.forename: Ernest
authors.initials: E
authors.lastname: Montbrió
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D016008:Statistical Distributions