Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators

We consider the effect of an external periodic force on chimera states in the phase oscillator model proposed in [Phys. Rev. Lett, v. 101, 00319007 (2008)].Using the Ott – Antonsen reduction, the dynamical equations for the global order parametercharacterizing the degree of synchronization are constructed. The frequency locking by an external periodic force region isconstructed. The possibility of stable chimeras synchronization and unstable chimerasstabilization is established. The instability development of the chimera states leads to the appearance of breather chimeras or complete synchronization.