  We consider a system of aggregated clusters of particles, subjected to
coagulation and fragmentation processes with mass dependent rates. Each monomer
particle can aggregate with larger clusters, and each cluster can fragment into
individual monomers with a rate directly proportional to the aggregation rate.
The dynamics of the cluster densities is governed by a set of Smoluchowski
equations, and we consider the addition of a source of monomers at constant
rate. The whole dynamics can be reduced to solving a unique non-linear
differential equation which displays self-oscillations in a specific range of
parameters, and for a number of distinct clusters in the system large enough.
This collective phenomenon is due to the presence of a fluctuating damping
coefficient and is closely related to the Li\'enard self-oscillation mechanism
observed in a more general class of physical systems such as the van der Pol
oscillator.
