论文标题
具有高阶相互作用的库拉马托模型中广泛的多群体的频谱
Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions
论文作者
论文摘要
相位振荡器的全球耦合集合是在各种应用中建模同步和集体行为的有用工具。随着对简单相互作用的兴趣（即三个或多个单位之间的非添加，高阶相互作用）的兴趣继续增长，我们研究了库拉莫托模型的扩展，其中振荡器通过三路相互作用通过表现出新型动力学性能，包括聚类，多差和突破性的desynChription synchronchronications耦合。在这里，我们通过在热力学极限中研究其光谱特性，对各种多簇状态的稳定性进行了严格的描述。与经典的库拉莫托模型不同，具有无限支撑的固有频率分布会产生一群漂移的振荡器，从而保证一部分光谱位于假想轴上，从而产生了中性稳定或不稳定的解决方案。另一方面，具有有限支撑的固有频率分布允许完全相锁状态，其频谱是真实的，并且可能是线性稳定或不稳定的。
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order interactions between three or more units) continues to grow we study an extension of the Kuramoto model where oscillators are coupled via three-way interactions that exhibits novel dynamical properties including clustering, multistability, and abrupt desynchronization transitions. Here we provide a rigorous description of the stability of various multicluster states by studying their spectral properties in the thermodynamic limit. Not unlike the classical Kuramoto model, a natural frequency distribution with infinite support yields a population of drifting oscillators, which in turn guarantees that a portion of the spectrum is located on the imaginary axes, resulting in neutrally stable or unstable solutions. On the other hand, a natural frequency distribution with finite support allows for a fully phase-locked state, whose spectrum is real and may be linearly stable or unstable.
