Nontrivial Periodic Coherent State in Globally Coupled Oscillators.

In this work, we study the mean-field Kuramoto model with attractive (positive) and repulsive (negative) coupling strengths under an external pinning force. We consider the coupling strengths correlate with the natural frequencies of oscillators. It is found that the interplay between the correlations and the pinning force induces multistable coherent behaves like different forms of traveling wave states, stationary synchronous and novel non-stationary dynamical behave: a nontrivial periodic coherent state. The nontrivial periodic coherent state can be depicted by the phase distributions of oscillators, the phase distributions oscillate in a confined region periodically. Finally, the dynamical distribution regions of the system with the parameter scale are demonstrated. [ABSTRACT FROM AUTHOR]