  We analyze synchronization between two interacting populations of different
phase oscillators. For the important case of asymmetric coupling functions, we
find a much richer dynamical behavior compared to that of symmetrically coupled
populations of identical oscillators (Okuda and Kuramoto, 1991). It includes
three types of bistabilities, higher order entrainment and the existence of
states with unusual stability properties. All possible routes to
synchronization of the populations are presented and some stability boundaries
are obtained analytically.
