  In this paper we analyze a coupled system between a transport equation and an
ordinary differential equation with time delay (which is a simplified version
of a model for kidney blood flow control). Through a careful spectral analysis
we characterize the region of stability, namely the set of parameters for which
the system is exponentially stable. Also, we perform a bifurcation analysis and
determine some properties of the stable steady state set and the limit cycle
oscillation region. Some numerical examples illustrate the theoretical results.
