Using a rate-equation model we numerically evaluate the carrier concentration and photon number in an integrated two-section semiconductor laser, and analyse its dynamics in three-dimensional phase space. The simulation comprises compact model descriptions extracted from a commercially-available generic InP technology platform, allowing us to model an applied reverse-bias voltage to the saturable absorber. We use the model to study the influence of the injected gain current, reverse-bias voltage, and cavity mirror reflectivity on the excitable operation state, which is the operation mode desired for the laser to act as an all-optical integrated neuron. We show in phase-space that our model is capable of demonstrating four different operation modes, i.e. cw, self-pulsating and an on-set and excitable mode under optical pulse injection. In addition, we show that lowering the reflectivity of one of the cavity mirrors greatly enhances the control parameter space for excitable operation, enabling more relaxed operation parameter control and lower power consumption of an integrated two-section laser neuron.