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, that 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.

References in corpus (3)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• The Kuramoto model of coupled oscillators with a bi-harmonic coupling function
• Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

Cited by in corpus (4)

• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Reconstruction of a random phase dynamics network from observations
• Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions