  We present a time-dependent approach to the one-zone hadronic model in the
case where the photon spectrum is produced by ultrarelativistic protons
interacting with soft photons that are produced from protons and low magnetic
fields. Assuming that protons are injected at a certain rate in a homogeneous
spherical volume containing a magnetic field, the evolution of the system can
be described by five coupled kinetic equations, for protons, electrons,
photons, neutrons, and neutrinos. Photopair and photopion interactions are
modelled using the results of Monte-Carlo simulations and, in particular from
the SOPHIA code for the latter. The coupling of energy losses and injection
introduces a self-consistency in our approach and allows the study of the
comparative relevancy of processes at various conditions, the efficiency of the
conversion of proton luminosity to radiation, the resulting neutrino spectra,
and the effects of time variability on proton injection, among other topics. We
present some characteristic examples of the temporal behaviour of the system
and show that this can be very different from the one exhibited by leptonic
models. Furthermore, we argue that, contrary to the wide-held belief, there are
parameter regimes where the hadronic models can become quite efficient.
However, to keep the free parameters at a minimum and facilitate an in-depth
study of the system, we have only concentrated on the case where protons are
injected; i.e., we did not consider the effects of a co-accelerated leptonic
component.
