Non-standard scaling law of fluctuations in finite-size systems of globally coupled oscillators

TL;DR

This paper investigates a non-standard fluctuation scaling law in finite-size systems of globally coupled oscillators, identifying conditions for its occurrence and validating these through numerical simulations across various models.

Contribution

It clarifies the conditions under which a non-standard fluctuation scaling law appears in globally coupled oscillators and confirms these conditions via simulations.

Findings

Non-standard scaling law observed in synchronized states.

Conditions for the scaling law are identified.

Validation through numerical simulations of different models.

Abstract

Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a non-standard scaling law with respect to system size in a synchronized state of globally coupled non-identical phase oscillators [Nishikawa et al., Chaos $\boldsymbol{22}$, 013133 (2012)]. However, it is still unclear how widely this non-standard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems, and we validate the conditions by numerical simulations of several different models.