AI 中文总结
本文针对Stuart-Landau振子群体建立精确低维约化理论，两种情形可分别约化为三维和七维系统，能捕捉相位振子无法描述的含振幅的复杂非平衡动力学。
AI 中文摘要
本文针对Stuart-Landau振子群体建立了一套精确的低维约化理论。该理论涵盖两种情形：其一，耦合仅通过Stuart-Landau方程的系数引入；其二，耦合还通过这些系数之外的项引入。在合适的假设下，两种情形可分别精确约化为三维和七维系统。该约化适用的额外耦合项类别足够通用，能支持从聚类等广泛的集体动力学。特别地，本文提出的约化方法被证明可捕捉振幅起关键作用的动力学，这类动力学无法用相位振子群体或其低维约化来描述。此外，该框架还被证实是捕捉混沌等复杂非平衡动力学的有力工具。
英文摘要
This paper develops an exact low-dimensional reduction theory for populations of Stuart-Landau oscillators. The theory covers two cases: in one case, coupling enters only through the coefficients of the Stuart-Landau equations, and in the other, coupling also enters through terms outside those coefficients. Under suitable assumptions, the two cases can be reduced exactly to three and seven-dimensional systems, respectively. The class of additional coupling terms for which the reduction applies is sufficiently general to allow a broad range of collective dynamics, such as clustering. In particular, the present reduction is shown to capture dynamics in which amplitude plays an essential role and which cannot be described by populations of phase oscillators or their low-dimensional reductions. The proposed framework is also shown to be a powerful tool for capturing complex nonequilibrium dynamics such as chaos.
Comments15 pages, 2 figures, including Supplemental Material
