  In this paper we address the exponential stability of a system of transport
equations with intermittent damping on a network of $N \geq 2$ circles
intersecting at a single point $O$. The $N$ equations are coupled through a
linear mixing of their values at $O$, described by a matrix $M$. The activity
of the intermittent damping is determined by persistently exciting signals, all
belonging to a fixed class. The main result is that, under suitable hypotheses
on $M$ and on the rationality of the ratios between the lengths of the circles,
such a system is exponentially stable, uniformly with respect to the
persistently exciting signals. The proof relies on an explicit formula for the
solutions of this system, which allows one to track down the effects of the
intermittent damping.
