论文标题
库拉马托模型中混合的不稳定性：从分叉到模式
Instability of mixing in the Kuramoto model: From bifurcations to patterns
论文作者
论文摘要
我们研究了在大图上具有随机固有频率的耦合相振荡器的库拉莫托模型中混合模型中混合稳定性丧失后观察到的模式，这也可以是随机的。我们表明，新兴模式是通过两个独立的机制来形成的，由频率分布的形状和基础图序列的限制结构确定。具体而言，我们确定了两个嵌套的特征值问题，它们的特征向量（不稳定模式）决定了新生模式的结构。通过在某些图上使用单峰和双峰频率分布的Kuramoto模型的数值实验的结果进行了分析。
We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which can also be random. We show that the emergent patterns are formed via two independent mechanisms determined by the shape of the frequency distribution and the limiting structure of the underlying graph sequence. Specifically, we identify two nested eigenvalue problems whose eigenvectors (unstable modes) determine the structure of the nascent patterns. The analysis is illustrated with the results of the numerical experiments with the Kuramoto model with unimodal and bimodal frequency distributions on certain graphs.
