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arXiv · 1512.01321

Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry

Christian Bick
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Abstract

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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Christian Bick. 2017-02-02. Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry. https://doi.org/10.1007/s00332-016-9345-2

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