The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.

中文翻译：

---

角频率的各向同性和具有破碎对称性的弱嵌合体。

弱嵌合体的概念为有限个相位振荡器网络中的嵌合体状态提供了一个易于理解的定义。在这里，我们通过根据其角频率矢量的各向同性来表征解，从而将弱嵌合体的定义推广到更通用的等变动力学系统，对于耦合相位振荡器，角频率矢量由矢量场的平均值给出沿着轨迹。解决方案的对称性自动意味着角频率同步。我们通过给出不存在偶合相位振荡器瞬时或整定对称性的弱嵌合体的结果，表明这种对称性的存在是不必要的。而且，