发表机构
University of Namur; Starling Research Institute（那慕尔大学; 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
本研究揭示一维swarmalator模型除已知三种宏观态外，还存在隐藏的稳定平衡态族，它们局部稳健但全局难以达到，扩展了该模型的状态理解。
AI 中文摘要
一维swarmalator模型通常通过三种宏观状态来理解：同步、相位波和异步。我们证明，相同的模型还包含更大的一组隐藏的稳定平衡态——q-扭转态和m-簇态族——随机初始条件几乎无法达到这些状态，因为许多状态嵌入在全局盆地消失的退化中性流形中。然而，它们在局部上是稳健的：在每坐标振幅的高斯扰动{\epsilon}下，它们的生存半径仅以代数方式缩小，即1/q和1/m，这与最近邻Kuramoto环上扭转态的高斯盆地和缠绕上限形成鲜明对比，这两者都被平均场耦合移除。块循环雅可比矩阵以闭式形式确定了稳定性，远踢实验表明这些盆地是紧凑的核心而非触手状集合。因此，扩展swarmalator模型中报告的几种模式已经存在于最小模型中，无论是稳定的还是中性稳定的。
英文摘要
The one-dimensional swarmalator model is usually understood through three macroscopic states: synchrony, the phase wave, and asynchrony. We show that the identical model also contains a much larger set of hidden stable equilibria - families of q-twisted and m-clustered states - which random initial conditions almost never reach, because many are embedded in a degenerate neutral manifold of vanishing global basin. They are nonetheless locally robust: under Gaussian perturbations of per-coordinate amplitude ε their survival radii shrink only algebraically, as 1/q and 1/m, in sharp contrast to the Gaussian basins and winding ceiling of twisted states on a nearest-neighbour Kuramoto ring, both removed by mean-field coupling. A block-circulant Jacobian fixes the stability in closed form, and far-kick experiments indicate the basins are compact cores rather than tentacled sets. Several patterns reported in extended swarmalator models thus already exist, stable or neutrally stable, in the minimal one.
