  The hadronic model of Active Galactic Nuclei and other compact high energy
astrophysical sources assumes that ultra-relativistic protons,
electron-positron pairs and photons interact via various hadronic and
electromagnetic processes inside a magnetized volume, producing the
multiwavelength spectra observed from these sources. A less studied property of
such systems is that they can exhibit a variety of temporal behaviours due to
the operation of different feedback mechanisms. We investigate the effects of
one possible feedback loop, where \gamma-rays produced by photopion processes
are being quenched whenever their compactness increases above a critical level.
This causes a spontaneous creation of soft photons in the system that result in
further proton cooling and more production of \gamma-rays, thus making the loop
operate. We perform an analytical study of a simplified set of equations
describing the system, in order to investigate the connection of its temporal
behaviour with key physical parameters. We also perform numerical integration
of the full set of kinetic equations verifying not only our analytical results
but also those of previous numerical studies. We find that once the system
becomes `supercritical', it can exhibit either a periodic behaviour or a damped
oscillatory one leading to a steady state. We briefly point out possible
implications of such a supercriticality on the parameter values used in Active
Galactic Nuclei spectral modelling, through an indicative fitting of the VHE
emission of blazar 3C 279.
