  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 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.
