Frequency synchronization in random oscillator network

TL;DR

This paper investigates frequency synchronization in randomly coupled oscillator networks, deriving conditions for synchronization and revealing that in scale-free networks with certain parameters, the critical coupling constant approaches zero, supported by numerical simulations.

Contribution

It provides a mean-field analysis of synchronization conditions and uncovers that the critical coupling constant vanishes in scale-free networks with degree exponent between 2 and 3.

Findings

Critical coupling constant K approaches 0 in certain scale-free networks.

Mean-field analysis yields sufficient conditions for synchronization.

Numerical simulations confirm analytical results.

Abstract

We study the frequency-synchronization of randomly coupled oscillators. By analyzing the continuum limit, we obtain the sufficient condition for the mean-field type synchronization. We especially find that the critical coupling constant $K$ becomes 0 in the random scale free network, $P(k)\propto k^{-\gamma}$, if $2 < \gamma \le 3$. Numerical simulations in finite networks are consistent with these analysis.