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 in | Radiophysics and quantum electronics Vol. 61; no. 8-9; pp. 640 - 649 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.01.2019
Springer Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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). |
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ISSN: | 0033-8443 1573-9120 |
DOI: | 10.1007/s11141-019-09924-7 |