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We consider the effect of an external periodic force on chimera state in thephase oscillator model proposed by Abrams et al. [Phys. Rev. Lett, v. 101,00319007 (2008)]. Using the Ott--Antonsen reduction the dynamical equations forthe global order parameter characterizing the degree of synchronization areconstructed. The regions of the global order parameter frequency locking by anexternal periodic force are constructed. The possibility of stable chimerassynchronization and unstable chimeras stabilization are established.

Synchronization by external periodic force in ensembles of globally coupled phase oscillators