TY  - JOUR
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Chimera patterns in the Kuramoto-Battogtokh model
JF  - Journal of physics : A, Mathematical and theoretical
N2  - Kuramoto and Battogtokh (2002 Nonlinear Phenom. Complex Syst. 5 380) discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After a reformulation in terms of a local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating, spatially periodic chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in the form of one-and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only the simplest chimeras with one synchronous region are stable.
KW  - nonlocal coupled oscillators
KW  - chimera state
KW  - coarse-grained order parameter
KW  - Ott-Antonsen reduction
KW  - perturbation approach
KW  - linear stability analysis
Y1  - 2017
U6  - https://doi.org/10.1088/1751-8121/aa55f1
SN  - 1751-8113
SN  - 1751-8121
VL  - 50
IS  - 8
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Breathing chimera in a system of phase oscillators
JF  - JETP Letters
N2  - Chimera states consisting of synchronous and asynchronous domains in a medium of nonlinearly coupled phase oscillators have been considered. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. The direct numerical simulation has shown that these structures under certain conditions are transformed to oscillatory (breathing) chimera regimes because of the development of instability.
Y1  - 2017
U6  - https://doi.org/10.1134/S0021364017180059
SN  - 0021-3640
SN  - 1090-6487
VL  - 106
SP  - 393
EP  - 399
PB  - Pleiades Publ.
CY  - New York
ER  -