@article{SmirnovOsipovPikovskij2018,
  author    = {Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij},
  title     = {Solitary synchronization waves in distributed oscillator populations},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.062222},
  pages     = {062222-1 -- 062222-7},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{BolotovSmirnovOsipovetal.2018,
  author    = {Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij},
  title     = {Simple and complex chimera states in a nonlinearly coupled oscillatory medium},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5011678},
  pages     = {9},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{GrinesOsipovPikovskij2018,
  author    = {Grines, Evgeny and Osipov, Grigory V. and Pikovskij, Arkadij},
  title     = {Describing dynamics of driven multistable oscillators with phase transfer curves},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {10},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5037290},
  pages     = {6},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}