@article{Omel'chenkoOcampoEspindolaKiss2021,
  author    = {Omel'chenko, Oleh and Ocampo-Espindola, Jorge Luis and Kiss, Istv{\´a}n Z.},
  title     = {Asymmetry-induced isolated fully synchronized state in coupled oscillator populations},
  series = {Physical review E : covering statistical, nonlinear, biological, and soft matter physics},
  volume    = {104},
  journal   = {Physical review E : covering statistical, nonlinear, biological, and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {Woodbury, NY},
  issn      = {2470-0045; 2470-0061; 1538-4519},
  doi       = {10.1103/PhysRevE.104.L022202},
  pages     = {6},
  year      = {2021},
  abstract  = {A symmetry-breaking mechanism is investigated that creates bistability between fully and partially synchronized states in oscillator networks. Two populations of oscillators with unimodal frequency distribution and different amplitudes, in the presence of weak global coupling, are shown to simplify to a modular network with asymmetrical coupling. With increasing the coupling strength, a synchronization transition is observed with an isolated fully synchronized state. The results are interpreted theoretically in the thermodynamic limit and confirmed in experiments with chemical oscillators.},
  language  = {en}
}
@article{Omel'chenko2022,
  author    = {Omel'chenko, Oleh},
  title     = {Mathematical framework for breathing chimera states},
  series = {Journal of nonlinear science},
  volume    = {32},
  journal   = {Journal of nonlinear science},
  number    = {2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0938-8974},
  doi       = {10.1007/s00332-021-09779-1},
  pages     = {34},
  year      = {2022},
  abstract  = {About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence-incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott-Antonsen reduction technique.},
  language  = {en}
}