论文标题
关于具有相同振荡器的库拉莫托模型的连续版本的解决方案
On solutions to the continuum version of the Kuramoto model with identical oscillators
论文作者
论文摘要
Kuramoto模型在相耦合振荡器的群体中提供了新兴同步的具体数学实现。由于库拉莫托的出版物\ textit {振荡，波和湍流}，研究人员一直致力于更好地表征解决方案动力学。在本文中，我们将特征的方法与迭代技术结合在一起，以证明振荡器相同并以限制性的特征来证明库拉莫托模型的连续版本的存在和唯一性。反过来，模型表征通过子和超级解决方案提供了对系统的全局渐近分析。我们认为，此处开发的独特模型分析方法有可能在其他更复杂的库拉莫托模型的其他更复杂的版本上产生新的结果。
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to better characterize solution dynamics. In this paper, we combine the method of characteristics with an iterative technique to prove existence and uniqueness of solutions to the continuum version of the Kuramoto model in the special case where oscillators are identical and characterize the oscillator density in terms of a limiting projected characteristic. The model characterization, in turn, provides for global asymptotic analysis of the system via sub and super solutions. We believe the unique approach to model analysis developed here has the potential to yield novel results on other more complex versions of the extensively studied Kuramoto model.
