利用时变拓扑特征计算耦合振子的相位动力学
Evaluating the phase dynamics of coupled oscillators via time-variant topological features
摘要：
通过描述耦合振子中的相位动力学，我们可以深入了解复杂系统的基本现象。振荡系统中的集体动力学通常用序参量来描述，这不足以识别更具体的行为。为了改善这种情况，我们提出了一种拓扑方法，构造描述振荡器相位演化的定量特征。这里，相位数据每次都被映射到高维空间中，并且随后从映射的点提取描述数据的形状的拓扑特征。通过在拓扑特征空间中增加演化时间作为额外的维数，将这些特征扩展为时变拓扑特征。时变特征为相位动力学的演化提供了重要的见解。结合这些功能与核方法，我们描述了多集群同步动力学在早期的进化阶段。最后，我们证明了我们的方法可以定性地解释嵌合态。实验结果证实了我们的方法优于基于序参量的方法，特别是当可用数据仅限于早期动力学时。
英文摘要：
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multi-clustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics.
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