论文标题
与惯性的库拉莫托模型中的分叉和模式
Bifurcations and patterns in the Kuramoto model with inertia
论文作者
论文摘要
在这项工作中，我们在收敛的图系上使用惯性分析了库拉莫托模型（KM）。假定从概率分布中对单个振荡器的固有频率进行采样。另外，给定的图也可能是随机的，它分配了网络连接。与原始km一样，在具有惯性的模型中，弱耦合方案具有混合特征，当所有振荡器的相位（但不是速度）均围绕单位圆均匀分布时，网络状态（但不是速度）。我们研究模式，当混合时，在耦合强度的变化下会失去稳定性。我们在模型中确定了具有多模式内在频率分布的模型中的干草叉（PF）和Andronov-Hopf（AH）分叉。为此，我们结合了线性稳定性分析和Penrose图，这是一种用于研究混合稳定性的几何技术。我们表明，分叉的类型和新生的时空模式取决于内在频率分布和网络连接的定性特性的相互作用。
In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given graph, which may also be random, assigns network connectivity. As in the original KM, in the model with inertia, the weak coupling regime features mixing, the state of the network when the phases (but not velocities) of all oscillators are distributed uniformly around the unit circle. We study patterns, which emerge when mixing loses stability under the variation of the strength of coupling. We identify a pitchfork (PF) and an Andronov-Hopf (AH) bifurcations in the model with multimodal intrinsic frequency distributions. To this effect, we use a combination of the linear stability analysis and Penrose diagrams, a geometric technique for studying stability of mixing. We show that the type of a bifurcation and a nascent spatiotemporal pattern depend on the interplay of the qualitative properties of the intrinsic frequency distribution and network connectivity.
