title: Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.
abstract: We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24, D-14476, Potsdam, Germany.|Department of Cell Biology and Neuroscience, University of California Riverside, 900 University Ave., Riverside, California 92521, USA.|Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod, Russia.
authors.forename: Maxim
authors.initials: M
authors.lastname: Komarov
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24, D-14476, Potsdam, Germany.|Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod, Russia.
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky
mesh_terms: D003198:Computer Simulation; D017711:Nonlinear Dynamics; D010507:Periodicity; D013816:Thermodynamics