  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.
