振子系综中周期轨道的连续性和持续性
Continua and persistence of periodic orbits in ensembles of oscillators
摘要：
某些耦合同振子系统，如Kuramoto-Sakaguchi或主动转子模型，具有Watanabe-Strogatz可积的显着性质。我们证明了这样的系统，耦合通过一个全球的序参数，功能正常吸引不变流形是由周期轨道叶状。这使我们能够研究的渐近动力学的一般合奏的全同振子应用平均理论。对于主动转子模型，扰动只会导致两千多个持续轨道，其中一个会导致splay态动力学。这揭示了以前观察到的splay状态的持久性和典型行为。
英文摘要：
Certain systems of coupled identical oscillators like the Kuramoto-Sakaguchi or the active rotator model possess the remarkable property of being Watanabe-Strogatz integrable. We prove that such systems, which couple via a global order parameter, feature a normally attracting invariant manifold that is foliated by periodic orbits. This allows us to study the asymptotic dynamics of general ensembles of identical oscillators by applying averaging theory. For the active rotator model, perturbations result in only finitely many persisting orbits, one of them giving rise to splay state dynamics. This sheds some light on the persistence and typical behavior of splay states previously observed.
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