Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling

摘要

We report on finite-sized-induced transitions to synchrony in a population ofphase oscillators coupled via a nonlinear mean field, which microscopically isequivalent to a hypernetwork organization of interactions. Using aself-consistent approach and direct numerical simulations, we argue that atransition to synchrony occurs only for finite-size ensembles, and disappearsin the thermodynamic limit. For all considered setups, that include purelydeterministic oscillators with or without heterogeneity in natural oscillatoryfrequencies, and an ensemble of noise-driven identical oscillators, weestablish scaling relations describing the order parameter as a function of thecoupling constant and the system size.