Maxim Bolotov
Nizhny Novgorod State University
Publications:
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Abramov S. S., Bolotov M. I., Smirnov L. A.
Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators
2024, vol. 29, no. 6, pp. 901-912
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.
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Bolotov D. I., Bolotov M. I., Smirnov L. A., Osipov G. V., Pikovsky A.
Twisted States in a System of Nonlinearly Coupled Phase Oscillators
2019, vol. 24, no. 6, pp. 717-724
Abstract
We study the dynamics of the ring of identical phase oscillators with nonlinear
nonlocal coupling. Using the Ott – Antonsen approach, the problem is formulated as a system
of partial derivative equations for the local complex order parameter. In this framework, we
investigate the existence and stability of twisted states. Both fully coherent and partially
coherent stable twisted states were found (the latter ones for the first time for identical
oscillators). We show that twisted states can be stable starting from a certain critical value
of the medium length, or on a length segment. The analytical results are confirmed with direct
numerical simulations in finite ensembles.
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