Pazó Diego, Montbrió Ernest
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046215. doi: 10.1103/PhysRevE.80.046215. Epub 2009 Oct 23.
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.
我们研究了具有自然频率双峰分布的Kuramoto模型中的同步转变。先前的研究得出结论，如果双峰分布由于中心凹陷较浅而接近单峰分布，该模型会表现出滞后相变。在这里我们表明，当中心凹陷的宽度而非深度趋于零时，接近单峰 - 双峰边界并不一定意味着存在滞后现象。我们通过对具有合适双峰分布族的Kuramoto模型进行详细研究得出了这一结论。
