  We present a novel form of collective oscillatory behavior in the kinetics of
irreversible coagulation with a constant input of monomers and removal of large
clusters. For a broad class of collision rates, this system reaches a
non-equilibrium stationary state at large times and the cluster size
distribution tends to a universal form characterised by a constant flux of mass
through the space of cluster sizes. Universality, in this context, means that
the stationary state becomes independent of the cut-off as the cut-off grows.
This universality is lost, however, if the aggregation rate between large and
small clusters increases sufficiently steeply as a function of cluster sizes.
We identify a transition to a regime in which the stationary state vanishes as
the cut-off grows. This non-universal stationary state becomes unstable,
however, as the cut-off is increased and undergoes a Hopf bifurcation. After
this bifurcation, the stationary kinetics are replaced by persistent and
periodic collective oscillations. These oscillations carry pulses of mass
through the space of cluster sizes. As a result, the average mass flux remains
constant. Furthermore, universality is partially restored in the sense that the
scaling of the period and amplitude of oscillation is inherited from the
dynamical scaling exponents of the universal regime. The implications of this
new type of long-time asymptotic behaviour for other driven non-equilibrium
systems are discussed.
