Stability diagram for the forced Kuramoto model
Stability diagram for the forced Kuramoto model
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DOI：
10.1063/1.3049136
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发表时间：
2008-12-01
期刊：
影响因子：
2.9
通讯作者：
Strogatz, Steven H.
中科院分区：
文献类型：
--
作者：
Childs, Lauren M.;Strogatz, Steven H.
我们分析周期性强迫 Kuramoto 模型。该系统由无限数量的相位振荡器组成，具有随机固有频率、全局正弦耦合和外部正弦强迫。它代表了物理、化学和生物学中许多现象的理想化，其中相互同步与强制同步竞争。换句话说，群体中的振荡器试图彼此同步，同时也试图锁定外部驱动器。先前对强迫仓本模型的研究发现了两种主要类型的吸引子，称为强迫夹带和互夹带，但它们之间分叉的细节尚不清楚。在这里，我们针对无限维动力学崩溃为二维系统的特殊情况，对模型进行了完整的分岔分析。获得了 Hopf、鞍节点和 Takens-Bogdanov 分岔位置的精确结果。由此产生的稳定性图与弱非线性受迫范德波尔振荡器的稳定性图极为相似。
We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.