Before revision:  To determine their relationship, we firstly determine the network instabilities that give rise to oscillations, and the set of false bifurcationsthat occur beyond this onset.
After revision:  To determine their relationship, we firstly determine the network instabilities that give rise to oscillations, and the so-called `false bifurcations' (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset.