  We consider large networks of theta neurons on a ring, synaptically coupled
with an asymmetric kernel. Such networks support stable "bumps" of activity,
which move along the ring if the coupling kernel is asymmetric. We investigate
the effects of the kernel asymmetry on the existence, stability and speed of
these moving bumps using continuum equations formally describing infinite
networks. Depending on the level of heterogeneity within the network we find
complex sequences of bifurcations as the amount of asymmetry is varied, in
strong contrast to the behaviour of a classical neural field model.
