  Mixed positive and negative feedback loops are often found in biological
systems which support oscillations. In this work we consider a prototype of
such systems, which has been recently found at the core of many genetic
circuits showing oscillatory behaviour. Our model consists of two interacting
species A and B, where A activates not only its own production, but also that
of its repressor B. While the self-activation of A leads already to a bistable
unit, the coupling with a negative feedback loop via B makes the unit
frustrated. In the deterministic limit of infinitely many molecules, such a
bistable frustrated unit is known to show excitable and oscillatory dynamics,
depending on the maximum production rate of A which acts as a control
parameter. We study this model in its fully stochastic version and we find
oscillations even for parameters which in the deterministic limit are deeply in
the fixed-point regime. The deeper we go into this regime, the more irregular
these oscillations are, becoming finally random excitations whenever
fluctuations allow the system to overcome the barrier for a large excursion in
phase space. The fluctuations can no longer be fully treated as a perturbation.
The smaller the system size (the number of molecules), the more frequent are
these excitations. Therefore, stochasticity caused by demographic noise makes
this unit even more flexible with respect to its oscillatory behaviour.
