标题： 异质性在高阶耦合的Kuramoto网络中诱导单眼状态 显示英文标题

标题： Heterogeneity Induces Cyclops States in Kuramoto Networks with Higher-Mode Coupling

摘要： 无序通常被视为集体动力学的有害因素，但近期研究表明异质性可以增强网络同步。 然而，它在稳定非平凡合作模式中的建设性作用尚未得到充分探索。 在本信中，我们展示即使在相同振荡器情况下这些状态不稳定的情况下，振荡器之间的频率异质性可以在高阶耦合的Kuramoto网络中诱导出稳定的独眼巨人态和聚类态。 [穆尼亚耶夫等人，Phys. Rev. Lett. 130, 107021 (2023)]引入的独眼巨人态特征是有两个同步簇和一个孤振子，需要微妙的相位平衡。 令人惊讶的是，异质性本身足以在广泛的失谐值范围内稳定这些模式，而无需通过其他形式的无序或外部调节来补偿。 我们引入了一种介观集体坐标方法，该方法将由孤振子的影响捕捉到的微观频率结构与平均场簇级稳定性联系起来。 这种建设性的方法识别出有利于异质性和合适的初始条件的范围，以诱导稳健的多状态动力学，为更广泛类别的异质生物和工程网络中的分析奠定了基础。 显示英文摘要

摘要： Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely unexplored. In this Letter, we show that frequency heterogeneity among oscillators can induce stable Cyclops and cluster states in Kuramoto networks with higher-mode coupling, even though these states are unstable in the identical oscillator case. Cyclops states, introduced in [Munyaev et al., Phys. Rev. Lett. 130, 107021 (2023)], feature two synchronized clusters and a solitary oscillator, requiring a delicate phase balance. Surprisingly, heterogeneity alone is sufficient to stabilize these patterns across a broad range of detuning values without needing to be compensated by other forms of disorder or external tuning. We introduce a mesoscopic collective coordinate approach that connects microscopic frequency structure, captured by the solitary oscillator's influence, with mean-field cluster-level stability. This constructive approach identifies favorable ranges of heterogeneity and suitable initial conditions for inducing robust multi-state dynamics, offering a foundation for their analysis in broader classes of heterogeneous biological and engineering networks.