发表机构
University of Namur; Starling Research Institute（南纳姆大学; 斯塔林研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨一维swarmalator模型在共同固有频率下延迟引起的多稳定性，发现延迟导致异步、相位波和同步三种状态在特定参数窗口共存，并在无稳定分支区域出现持续振荡。
AI 中文摘要
我们研究了当所有单元共享共同固有频率{\omega}时的一维延迟swarmalator模型。与零频率情况不同，{\omega}不能通过旋转框架变换消除，因为延迟相互作用保留了滞后期间累积的相位。结果是延迟Kuramoto模型的双阶参数类比：异步状态获得非相干瓣，同步状态成为旋转分支，即使空间和相位耦合都是排斥性的也保持稳定，并且相位波发展出狭窄的共振稳定带。这些延迟选择窗口重叠产生广泛的分支共存，包括在K=-J附近的一个狭窄窗口，其中所有三种典型状态——异步、相位波和同步——同时稳定。在没有典型分支稳定的区域中，阶参数持续振荡。
英文摘要
We study the delayed one-dimensional swarmalator model when all units share a common intrinsic frequency ω. Unlike the zero-frequency case, ω cannot be removed by a rotating-frame transformation because delayed interactions retain the phase accumulated over the lag. The result is a two-order-parameter analogue of the delayed Kuramoto model: the asynchronous state acquires incoherence lobes, the synchronized state becomes a rotating branch stable even when both the spatial and phase couplings are repulsive, and the phase wave develops narrow resonant stability bands. These delay-selected windows overlap to produce broad branch coexistence, including a narrow window near K=-J where all three canonical states-asynchronous, phase wave, and synchronized-are simultaneously stable. In regions where no canonical branch is stable, the order parameters oscillate persistently.
