Bick Christian
Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter, EX4 4QF UK.
J Nonlinear Sci. 2017;27(2):605-626. doi: 10.1007/s00332-016-9345-2. Epub 2016 Nov 10.
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.
弱嵌合体的概念为有限多个相位振子网络中的嵌合体状态提供了一个易于处理的定义。在此,我们通过根据角频率向量的各向同性来刻画解,将弱嵌合体的定义推广到更一般的等变动力系统类别——对于耦合相位振子,角频率向量由沿轨迹的向量场平均值给出。解的对称性自动意味着角频率同步。我们通过给出耦合相位振子不存在瞬时或逐点对称性的弱嵌合体存在性结果,表明这种对称性的存在并非必要。此外,我们构造了一个耦合函数,在具有广义耦合的弱耦合相位振子群体中产生无对称性的混沌弱嵌合体。