  In an oscillatory medium, a region which oscillates faster than its
surroundings can act as a source of outgoing waves. Such pacemaker-generated
waves can synchronize the whole medium and are present in many chemical and
biological systems, where they are a means of transmitting information at a
fixed speed over large distances. In this paper, we apply analytical tools to
investigate the factors that determine the speed of these waves. More
precisely, we apply singular perturbation and phase reduction methods to two
types of negative-feedback oscillators, one built on underlying bistability and
one including a time delay in the negative feedback. In both systems, we
investigate the influence of timescale separation on the resulting wave speed,
as well as the effect of size and frequency of the pacemaker region. We compare
our analytical estimates to numerical simulations which we described previously
[1].
