title: Multiplicity of singular synchronous states in the Kuramoto model of coupled oscillators.
abstract: We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24, D-14476 Potsdam, Germany and Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Maxim
authors.initials: M
authors.lastname: Komarov
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky