Hall thrusters are plasma-based devices that have established themselves as one of the most attractive and mature electric propulsion technologies for space applications. These devices often operate in a regime characterized by low frequency, large amplitude oscillations of the discharge current, which is commonly referred to as the ‘breathing mode’. The intensity of these oscillations depends on the thruster’s design and operating conditions and can reach values of the order of the average discharge current, posing issues for the thruster’s performance and for coupling with the driving electronics. A 0D model of the thruster discharge was developed to investigate the core physical mechanisms leading to the onset and sustenance of the breathing mode. The model was found to be capable of reproducing oscillations with characteristics in line with those observed in the breathing mode. In this work, we extend the use of the 0D model to investigate the effect of the magnetic field intensity and of different propellants on the system stability.