Synchronization in the presence of distributed delays

TL;DR

This paper investigates how distributed delays in coupling affect synchronization in networks of identical oscillators, revealing that mean delay influences stability while distribution shape impacts dynamics.

Contribution

It demonstrates that synchronization frequency and stability depend solely on the mean delay, but the shape of the delay distribution influences the synchronization dynamics.

Findings

Synchronization frequency depends only on mean delay

Stability of synchronized states is determined by mean delay

Synchronization rate can be maximized at specific coupling strengths

Abstract

We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean of the delay distribution. However, synchronization dynamics is sensitive to the shape of the distribution. In the presence of coupling delays, the synchronization rate can be maximal for a specific value of the coupling strength.