Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
Adaptation and Self-Organizing Systems
2017-03-01 v1 Pattern Formation and Solitons
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.
Keywords
Cite
@article{arxiv.1702.08776,
title = {Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling},
author = {Maxim Komarov and Arkady Pikovsky},
journal= {arXiv preprint arXiv:1702.08776},
year = {2017}
}