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

Semyon S. Abramov, Maxim I. Bolotov, Lev A. Smirnov

Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, av. Gagarina 23, 603022 Nizhny Novgorod, Russia

Abstract: 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 parameter characterizing the degree of synchronization are constructed. The frequency locking by an external periodic force region is constructed. The possibility of stable chimeras synchronization and unstable chimeras stabilization is established. The instability development of the chimera states leads to the appearance of breather chimeras or complete synchronization.

Keywords: external force, synchronization, stabilization, chimera state, phase oscillator

MSC: 34C15

Received: 20.02.2024
Accepted: 20.10.2024

Language: English

DOI: 10.1134/S1560354724570012