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  -