论文标题
关于密集网络上有限的库拉莫托模型的关键耦合
On the Critical Coupling of the Finite Kuramoto Model on Dense Networks
论文作者
论文摘要
Kuramoto模型是耦合振荡器同步的最突出的模型之一。长期以来，一直是一个研究热点，可以理解固有频率，振荡器之间的相互作用以及网络拓扑之间的相互作用如何决定同步的开始。在本文中，我们调查了库拉莫托振荡器在确定性密集网络上的关键耦合，这被视为来自相同振荡器的全部对所有网络的自然概括。我们提供了足够的条件，在该条件下，具有非相同振荡器的库拉莫托模型具有一个独特而稳定的平衡。此外，这种平衡具有相位的凝聚力，并具有局部指数同步。我们对随机网络和循环网络上的库拉莫托模型进行数值模拟，以补充我们的理论分析，并为将来的研究提供见解。
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology determine the onset of synchronization. In this paper, we investigate the critical coupling of Kuramoto oscillators on deterministic dense networks, viewed as a natural generalization from all-to-all networks of identical oscillators. We provide a sufficient condition under which the Kuramoto model with non-identical oscillators has one unique and stable equilibrium. Moreover, this equilibrium is phase cohesive and enjoys local exponential synchronization. We perform numerical simulations of the Kuramoto model on random networks and circulant networks to complement our theoretical analysis and provide insights for future research.
