期刊
JOURNAL OF NONLINEAR SCIENCE
卷 27, 期 2, 页码 605-626出版社
SPRINGER
DOI: 10.1007/s00332-016-9345-2
关键词
Oscillator networks; Phase oscillators; Weak chimera; Symmetry; Asymptotic average frequencies
资金
- People Programme (Marie Curie Actions) of the European Union [626111]
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.
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