@article{TyulkinaGoldobinKlimenkoetal.2019,
  author    = {Tyulkina, Irina V. and Goldobin, Denis S. and Klimenko, Lyudmila S. and Pikovskij, Arkadij},
  title     = {Two-Bunch Solutions for the Dynamics of Ott-Antonsen Phase Ensembles},
  series = {Radiophysics and Quantum Electronics},
  volume    = {61},
  journal   = {Radiophysics and Quantum Electronics},
  number    = {8-9},
  publisher = {Springer},
  address   = {New York},
  issn      = {0033-8443},
  doi       = {10.1007/s11141-019-09924-7},
  pages     = {640 -- 649},
  year      = {2019},
  abstract  = {We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott-Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott-Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto-Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch "Abrams chimeras" for imperfect identity (in the latter case, the one-bunch chimeras become attractive).},
  language  = {en}
}