Radiophysics and Quantum Electronics

, Volume 61, Issue 8–9, pp 640–649 | Cite as

Two-Bunch Solutions for the Dynamics of Ott–Antonsen Phase Ensembles

  • I. V. TyulkinaEmail author
  • D. S. Goldobin
  • L. S. Klimenko
  • A. S. Pikovsky

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).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • I. V. Tyulkina
    • 1
    Email author
  • D. S. Goldobin
    • 1
    • 2
  • L. S. Klimenko
    • 1
    • 2
  • A. S. Pikovsky
    • 3
    • 4
  1. 1.State University of PermPermRussia
  2. 2.Institute for Mechanics of Continuous MediaUral Branch of the Russian Academy of SciencesPermRussia
  3. 3.Potsdam UniversityPotsdamGermany
  4. 4.N. I. Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

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