  Non-linear behavior in interstellar chemical models has been recognized for
25 years now. Different mechanisms account for the possibility of multiple
fixed-points at steady state, characterized by the ionization degree of the
gas. Chemical oscillations are also a natural behaviour of non-linear chemical
models. We study under which conditions spontaneous sustained chemical
oscillations are possible, and what kind of biffurcations lead to, or quench,
the occurrence of such oscillations. Methods. The well known Ordinary
Differential Equations (ODE) integrator VODE is used to explore initial
conditions and parameter space in a gas phase chemical model of a dark
interstellar cloud. We recall that the time evolution of the various chemical
abundances under fixed temperature conditions depends on the density over
cosmic ionization rate nH/{\zeta} ratio. We also report the occurrence of
naturally sustained oscillations for a limited but well defined range of
control parameters. The period of oscillations is within the range of
characteristic time scales of interstellar processes and could lead to
spectacular resonances in time dependent models. Reservoir species (C, CO, NH3,
...) oscillation amplitudes are generally less than a factor two. However,
these amplitudes reach a factor ten to thousand for low abundance species, e.g.
HCN, ND3, that may play a key role for diagnostic purposes.The mechanism
responsible for oscillations is tightly linked to the chemistry of nitrogen,
and requires long chains of reactions such as found in multi-deuteration
processes.
