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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- 11.D. S. Goldobin, A. V. Dolmatova, M. Rosenblum, and A. Pikovsky, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Dinam., 25, No. 6, 5 (2017).Google Scholar