Blocking and transmission of traveling flow-distributed-oscillation waves in an absolutely unstable flowing medium

For a flowing, self-oscillating medium, we study the competition between traveling flow-distributed-oscillation waves excited by periodic driving at the upstream boundary and bulk oscillations originating downstream from the boundary. As previously observed in the case of stationary driving, we find that there is a region in parameter space where boundary-driven traveling waves of sufficiently high amplitude can impose themselves on the entire medium despite the presence of an absolute instability, which otherwise tends to block information from upstream. For sufficiently low flow rates, however, the imposed waves are arrested at a nonlinear blocking transition. Unlike the stationary case, we find that the region of imposed waves extends well into regions where, according to the linear approximation, there should be no traveling waves at all. This suggests that the extinction of the traveling waves is analogous to a subcritical Hopf bifurcation.