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

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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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Authors and Affiliations

  1. State University of Perm, Perm, Russia

    I. V. Tyulkina, D. S. Goldobin & L. S. Klimenko

  2. Institute for Mechanics of Continuous Media, Ural Branch of the Russian Academy of Sciences, Perm, Russia

    D. S. Goldobin & L. S. Klimenko

  3. Potsdam University, Potsdam, Germany

    A. S. Pikovsky

  4. N. I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    A. S. Pikovsky

Authors
  1. I. V. Tyulkina
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  2. D. S. Goldobin
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  3. L. S. Klimenko
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  4. A. S. Pikovsky
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Corresponding author

Correspondence to I. V. Tyulkina.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 8–9, pp. 718–728, August–September 2018.

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Tyulkina, I.V., Goldobin, D.S., Klimenko, L.S. et al. Two-Bunch Solutions for the Dynamics of Ott–Antonsen Phase Ensembles. Radiophys Quantum El 61, 640–649 (2019). https://doi.org/10.1007/s11141-019-09924-7

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  • DOI: https://doi.org/10.1007/s11141-019-09924-7

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