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arXiv · 0904.3735

Existence of hysteresis in the Kuramoto model with bimodal frequency distributions

Diego Pazó·Ernest Montbrió
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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 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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Diego Pazó, Ernest Montbrió. 2009-04-23. Existence of hysteresis in the Kuramoto model with bimodal frequency distributions. https://doi.org/10.1103/physreve.80.046215

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