Symmetry-broken coherent state in a ring of nonlocally coupled identical oscillators

We report on a modulated coherent state in a ring of nonlocally coupled oscillators. Although the identical oscillators are all synchronized under the symmetric coupling, the phase configuration has an inhomogeneous structure. This symmetry-broken coherent state exists only for a nonlocal coupling with both attracting and repulsive interactions, depending on the distance between oscillators, and emerges via a continuous bifurcation from a uniformly coherent state. We analyze the existence and stability of the modulated coherent states on the basis of Ott-Antonsen equations for the local order parameter. Our theoretical results are verified using the numerical simulations.