Link-disorder fluctuation effects on synchronization in random networks

TL;DR

This paper studies how link-disorder fluctuations in random networks of oscillators influence synchronization, revealing that such fluctuations induce uncorrelated frequency-like noise and determine the finite-size scaling behavior.

Contribution

It demonstrates that link-disorder fluctuations cause a specific finite-size scaling exponent, matching the globally coupled case, through numerical and mean-field analysis.

Findings

Link-disorder fluctuations induce uncorrelated frequency fluctuations.

Finite-size scaling exponent is 5/2, identical to globally coupled systems.

Numerical simulations confirm the theoretical predictions.

Abstract

We consider one typical system of oscillators coupled through disordered link configurations in networks, i.e., a finite population of coupled phase oscillators with distributed intrinsic frequencies on a random network. We investigate collective synchronization behavior, paying particular attention to link-disorder fluctuation effects on the synchronization transition and its finite-size scaling (FSS). Extensive numerical simulations as well as the mean-field analysis have been performed. We find that link-disorder fluctuations effectively induce {\em uncorrelated random} fluctuations in frequency, resulting in the FSS exponent $\bar\nu=5/2$, which is identical to that in the globally coupled case (no link disorder) with frequency-disorder fluctuations.