The Kuramoto-Sakaguchi model for coupled phase oscillators with phase frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture the collective dynamics of finite-size Kuramoto-Sakaguchi models. We find that the inclusion of the effects of rogue oscillators is essential to obtain an accurate description, in contrast to the original Kuramoto model, where we show that their effects can be ignored. We further introduce a more accurate ansatz function to describe the shape of synchronized oscillators. Our results from this extended collective coordinate approach reduce in the thermodynamic limit to the well-known mean-field consistency relations. For finite networks we show that our model reduction describes the collective behavior accurately, reproducing the order parameter, the mean frequency of the synchronized cluster, and the size of the cluster at a given coupling strength, as well as the critical coupling strength for partial and for global synchronization.

中文翻译：

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仓本坂口模型的模型简化：非携带流氓振荡器的重要性。

经常在无限多个振荡器的热力学极限条件下研究带相位挫折的耦合相位振荡器的Kuramoto-Sakaguchi模型。在这里，我们扩展了一种基于集体坐标的模型简化方法，以捕获有限尺寸的仓本坂口模型的集体动力学。我们发现，与原始的仓本模型相比，包含无赖振荡器的影响对于获得准确的描述是必不可少的，在原始模型中，我们证明了可以忽略它们的影响。我们进一步介绍了更精确的ansatz函数来描述同步振荡器的形状。我们从这种扩展的集体坐标方法得出的结果将热力学极限降低到了众所周知的平均场一致性关系。