论文标题
基于力矩的有效方法，用于模拟无限的许多异质相振荡器
Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators
论文作者
论文摘要
通常描述了相位振荡器合奏的动力学，以考虑其无限尺寸的极限。但是，实际上，只有在可以应用Ott-Antonsen理论并且在有理功能下分布异质性时，该极限才能完全访问。在这项工作中，我们证明了基于矩的方案的实用性，以重现无限的许多振荡器的动力学。我们的分析专门针对高斯异质性，从而导致振荡器密度的傅里叶分解。傅立叶 - 热点遵守一组分层的普通微分方程。作为初步实验，在可解析的库拉莫托模型中测试了截断力矩系统和实施不同封闭的效果。基于力矩的方法被证明比直接模拟大型振荡器集合的效率要高得多。在两个说明性示例中利用了基于力矩的方法的便利性：（i）具有双峰频率分布的库拉莫托模型，以及（ii）“放大的库拉莫托模型”（具有非脚部相互作用）。在这两个系统中，我们通过直接数值整合人群获得了无法访问的新结果。
The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be applied, and the heterogeneity is distributed following a rational function. In this work we demonstrate the usefulness of a moment-based scheme to reproduce the dynamics of infinitely many oscillators. Our analysis is particularized for Gaussian heterogeneities, leading to a FourierHermite decomposition of the oscillator density. The Fourier-Hermite moments obey a set of hierarchical ordinary differential equations. As a preliminary experiment, the effects of truncating the moment system and implementing different closures are tested in the analytically solvable Kuramoto model. The moment-based approach proves to be much more efficient than the direct simulation of a large oscillator ensemble. The convenience of the moment-based approach is exploited in two illustrative examples: (i) the Kuramoto model with bimodal frequency distribution, and (ii) the 'enlarged Kuramoto model' (endowed with nonpairwise interactions). In both systems we obtain new results inaccessible through direct numerical integration of populations.
