论文标题
网络和相位对称性揭示了振幅动力学稳定解耦的振荡器簇
Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters
论文作者
论文摘要
振荡器网络显示复杂的同步模式。确定其稳定性通常需要结合网络耦合的对称性。我们超越了仅吸引网络自动形态组的分析，我们探索了从节点中动力学方程和对称性的相移不变性出现的同步模式。我们表明，这些非结构对称性简化了稳定性计算。我们分析了具有“脱钩”状态的相位振幅振荡器的环网络，在该状态下，由于动态演化方程中出现的取消，物理耦合的节点似乎独立起作用。我们确定该状态对于相位振幅振荡器的环可能是线性稳定的，但对于仅相位振荡器的环，否则这些状态否则需要明确的远距离，非局部或非相耦合。简而言之，振幅相互作用是距离稳定同步的关键。
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group, we explore synchronization patterns that emerge from the phase-shift invariance of the dynamical equations and symmetries in the nodes. We show that these nonstructural symmetries simplify stability calculations. We analyze a ring-network of phase-amplitude oscillators that exhibits a "decoupled" state in which physically-coupled nodes appear to act independently due to emergent cancellations in the equations of dynamical evolution. We establish that this state can be linearly stable for a ring of phase-amplitude oscillators, but not for a ring of phase-only oscillators that otherwise require explicit long-range, nonpairwise, or nonphase coupling. In short, amplitude-phase interactions are key to stable synchronization at a distance.
