发表机构
Max Planck Institute for Neurobiology of Behavior; Universidade Federal de São Paulo; University of Texas at Dallas; Fields Institute; Universidade Estadual Paulista; University of Lethbridge（马克斯·普朗克行为神经生物学研究所; 圣保罗联邦大学; 德克萨斯大学达拉斯分校; 菲尔兹研究所; 圣保罗州立大学; 莱斯布里奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对Kuramoto网络，提出结合连通性与相位延迟的复合矩阵谱可分析估计锁相状态吸引域大小，揭示了传统稳定性分析无法检测的多稳态与手性动力学。
AI 中文摘要
我们研究网络连通性与异质相位延迟如何塑造有限振子网络的时空动力学。相位延迟可破坏全局同步的稳定性，促进锁相模式的形成，包括具有均匀相位梯度的状态及这些模式的更复杂组合。然而，连通性与相位延迟如何共同决定网络选择何种状态仍不明确。本文中，我们表明结合连通性与相位延迟的复合矩阵的谱，不仅决定网络集体状态的线性稳定性，还决定其吸引域大小。这进而使得仅通过连通性与相位延迟就能对单个网络的锁相状态吸引域大小进行分析估计。将该框架应用于非局部网络与全局网络（包括随机相位延迟的情况），我们发现了多稳态与吸引域大小的强不对称性，揭示了传统稳定性分析无法检测的手性动力学。
英文摘要
We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronization and promote phase-locked patterns, including states with uniform phase gradients and more complex combinations of these modes. Yet, how connectivity and phase-delays jointly determine which states the network selects remains unclear. Here, we show that the spectrum of a composite matrix, which combines connectivity and phase-delays, governs not only the linear stability of the network's collective states but also their basin sizes. This, in turn, enables analytical estimates of basin size of phase-locked states for individual networks from connectivity and phase-delays alone. Applying this framework to nonlocal and global networks, including cases with random phase-delays, we uncover multistability and strong asymmetries in basin sizes, revealing chiral dynamics that conventional stability analysis cannot detect.
