The knowledge of the linewidth enhancement factor (alpha(H)-factor) is very important to understand the performance of semiconductor lasers. It affects several fundamental aspects such as the linewidth, the laser's behavior under optical feedback, the chirp under direct modulation and the occurrence of the filamentation. The dramatic variation in the alpha(H)-factor that has been reported for quantum dot lasers makes them an interesting subject for optical feedback studies. In the particular case of QD lasers, the carrier density is not clearly clamped at threshold. The lasing wavelength can switch from the ground state to the excited state as the current injection increases meaning that a carrier accumulation occurs in the ES even though lasing in the GS is still occurring. The purpose of the paper is to show that the exploitation of the nonlinear properties arising from quantum nanostructure based semiconductor lasers operating under external optical feedback can lead, under specific conditions, to a bifurcation of the modulation properties. Starting from the generalized rate equations under optical feedback, the laser's modulation response is determined. Under the short external cavity assumption, calculations show that large variations of the alpha(H)-factor can contribute to improve the dynamical properties such as the relaxation frequency as well as the laser's bandwidth. On the contrary, assuming the long external cavity situation, numerical results show that even small reflections in the percent range when combined to significant variations of the alpha(H)-factor alter the laser's modulation response.