TY  - JOUR
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Solitary synchronization waves in distributed oscillator populations
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We demonstrate the existence of solitary waves of synchrony in one-dimensional arrays of oscillator populations with Laplacian coupling. Characterizing each community with its complex order parameter, we obtain lattice equations similar to those of the discrete nonlinear Schrodinger system. Close to full synchrony, we find solitary waves for the order parameter perturbatively, starting from the known phase compactons and kovatons; these solutions are extended numerically to the full domain of possible synchrony levels. For nonidentical oscillators, the existence of dissipative solitons is shown.
Y1  - 2018
U6  - https://doi.org/10.1103/PhysRevE.98.062222
SN  - 2470-0045
SN  - 2470-0053
VL  - 98
IS  - 6
SP  - 062222-1
EP  - 062222-7
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Simple and complex chimera states in a nonlinearly coupled oscillatory medium
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. In terms of a local coarse-grained complex order parameter, the problem of finding stationary rotating nonhomogeneous solutions reduces to a third-order ordinary differential equation. This allows finding chimera-type and other inhomogeneous states as periodic orbits of this equation. Stability calculations reveal that only some of these states are stable. We demonstrate that an oscillatory instability leads to a breathing chimera, for which the synchronous domain splits into subdomains with different mean frequencies. Further development of instability leads to turbulent chimeras. Published by AIP Publishing.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5011678
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 4
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Grines, Evgeny
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Describing dynamics of driven multistable oscillators with phase transfer curves
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - Phase response curve is an important tool in the studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a perturbation, transitions from one oscillating mode to another one may occur. We define phase transfer curves to describe the phase shifts at such transitions. This allows for a construction of one-dimensional maps that characterize periodically kicked multistable oscillators. We show that these maps are good approximations of the full dynamics for large periods of forcing. Published by AIP Publishing.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5037290
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 10
PB  - American Institute of Physics
CY  - Melville
ER  -