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

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 equa...

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Published inRadiophysics and quantum electronics Vol. 61; no. 8-9; pp. 640 - 649
Main Authors Tyulkina, I. V., Goldobin, D. S., Klimenko, L. S., Pikovsky, A. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.01.2019
Springer
Springer Nature B.V
Subjects
Astronomy
Astrophysics and Astroparticles
Hadrons
Heavy Ions
Lasers
Mathematical analysis
Mathematical and Computational Physics
Nuclear Physics
Observations and Techniques
Optical Devices
Optics
Order parameters
Oscillators
Phase transitions
Photonics
Physics
Physics and Astronomy
Quantum Optics
System dynamics
Theoretical
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Summary: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).
ISSN:0033-8443
1573-9120
DOI:10.1007/s11141-019-09924-7