Boundaries for the primary saddle-node bifurcations related to the main resonances in pump--modulated laser diodes are obtained via numerical simulation. Our model contains explicitly the gain saturation and spontaneous emission terms and we focus on the effect that these terms have on the large signal modulation regime. We find that the spontaneous emission term strongly modifies the qualitative behavior of the instabilities boundaries, while the gain saturation factor manifests itself in the damping of relaxation oscillations and leads to a simple quantitative shift of boundaries.
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