Critical exponents in coupled phase-oscillator models on small-world networks

TL;DR

This paper investigates the critical exponents of synchronization transitions in coupled phase-oscillator models on small-world networks, revealing a universal critical exponent across different models and frequency distributions.

Contribution

It demonstrates that the universality class of the synchronization transition is reduced to one in small-world networks, regardless of the natural frequency distribution and coupling function complexity.

Findings

Number of universality classes is reduced to one in small-world networks.

Critical exponent is shared across models with up to second harmonic coupling.

Universality persists regardless of natural frequency distribution symmetry.

Abstract

A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the non-synchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a small-world network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in small-world networks irrespective of the order of links. Our numerical results suggest that the number of universality class is reduced to one and the critical exponent is shared in the considered models having coupling functions up to the second harmonics with unimodal and symmetric natural frequency distributions.