Extended finite-size scaling of synchronized coupled oscillators

TL;DR

This paper extends finite-size scaling analysis to the dynamics of coupled oscillators, providing a comprehensive understanding of phase synchronization and critical phenomena in the Kuramoto model.

Contribution

It introduces an extended finite-size scaling framework for the dynamics of coupled oscillators, allowing measurement of critical exponents and analysis of effects like frequency sampling and noise.

Findings

Determined critical coupling strength for synchronization.

Measured dynamic FSS exponents and thermodynamic critical exponents.

Confirmed effects of frequency sampling and noise on scaling behavior.

Abstract

We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with non-identical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of phase synchronization. In particular, we extend finite-size scaling (FSS) in the steady state to dynamics, determine critical exponents, and find the critical coupling strength. The dynamic scaling approach enables us to measure not only the FSS exponent associated with the correlation volume in finite systems but also thermodynamic critical exponents. Based on the extended FSS theory, we also discuss how the sampling of natural frequencies and thermal noise affect dynamic scaling, which is numerically confirmed.