@article{SmirnovOsipovPikovskij2017,
  author    = {Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij},
  title     = {Chimera patterns in the Kuramoto-Battogtokh model},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {50},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {8},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aa55f1},
  pages     = {10},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{BolotovSmirnovOsipovetal.2017,
  author    = {Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij},
  title     = {Breathing chimera in a system of phase oscillators},
  series = {JETP Letters},
  volume    = {106},
  journal   = {JETP Letters},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0021-3640},
  doi       = {10.1134/S0021364017180059},
  pages     = {393 -- 399},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}