title: Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions.
abstract: We discuss the desynchronization transition in networks of globally coupled identical oscillators with attractive and repulsive interactions. We show that, if attractive and repulsive groups act in antiphase or close to that, a solitary state emerges with a single repulsive oscillator split up from the others fully synchronized. With further increase of the repulsing strength, the synchronized cluster becomes fuzzy and the dynamics is given by a variety of stationary states with zero common forcing. Intriguingly, solitary states represent the natural link between coherence and incoherence. The phenomenon is described analytically for phase oscillators with sine coupling and demonstrated numerically for more general amplitude models.
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany and Institute of Mathematics and National Centre for Medical and Biotechnical Research, National Academy of Sciences of Ukraine, Kiev, Ukraine.
authors.forename: Yuri
authors.initials: Y
authors.lastname: Maistrenko
authors.affiliation: National University of "Kyiv-Mohyla Academy," Kiev, Ukraine and FEMTO-ST/Optics Department, University of Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France.
authors.forename: Bogdan
authors.initials: B
authors.lastname: Penkovsky
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Rosenblum
mesh_terms: D016000:Cluster Analysis; D017143:Fuzzy Logic; D017711:Nonlinear Dynamics; D010507:Periodicity