Existence of hysteresis in the Kuramoto model with bimodal frequency distributions.

Phys Rev E Stat Nonlin Soft Matter Phys 80(4 Pt 2):046215 (2009) PMID 19905423

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.