Synchronization in networks of mobile oscillators

TL;DR

This paper investigates how the changing topology in networks of mobile oscillators affects synchronization, highlighting the importance of the relative time scales of motion and synchronization for network design.

Contribution

It introduces a model analyzing the impact of agent motion on synchronization, revealing the significance of the interplay between topological change and local synchronization times.

Findings

Synchronization time increases when topological changes are slow.

Near the percolation transition, effects of motion on synchronization are more pronounced.

Spectral analysis confirms the impact of time scale trade-offs on synchronization.

Abstract

We present a model of synchronization in networks of autonomous agents where the topology changes due to agents motion. We introduce two time scales, one for the topological change and another one for local synchronization. If the former scale is much shorter, an approximation that averages out the effect of motion is available. Here we show, however, that the time required for synchronization achievement increases with respect to that approximation in the opposite case. We find that this effect is more important close to the continuum percolation transition point. The simulation results are confirmed by means of spectral analysis of the time dependent Laplacian matrix. Our results show that the trade-off between these two time scales, which have opposite effects on synchronization, should be taken into account for the design of mobile device networks.