On the stability of the Kuramoto model of coupled nonlinear oscillators
On the stability of the Kuramoto model of coupled nonlinear oscillators
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DOI：
10.23919/acc.2004.1383983
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发表时间：
2005-04
期刊：
影响因子：
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通讯作者：
A. Jadbabaie;N. Motee;Mauricio Barahona
中科院分区：
文献类型：
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作者：
A. Jadbabaie;N. Motee;Mauricio Barahona
我们提供了对耦合非线性振荡器的经典 Kuramoto 模型的分析，该模型超出了相同振荡器的所有网络的现有结果。我们的工作适用于具有不确定固有频率的任意互连拓扑的振荡器网络。使用谱图理论和控制理论的工具，我们证明，对于高于临界值的耦合，所有振荡器都会同步，从而导致所有相位差收敛到恒定值，无论是在固有频率相同还是不确定的情况下。我们还为耦合强度的临界值提供了一系列界限。
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We also provide a series of bounds for the critical values of the coupling strength.