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

Existence of hysteresis in the Kuramoto model with bimodal frequency distributions