We analyze a delay differential equation for the amplitude of the electrical field in order to understand recent experimental observations of low-frequency oscillations in a QD laser. The laser contains no saturable absorber section and exhibits no relaxation oscillations. We investigate the problem both analytically and numerically. We show that there exists a homoclinic bifurcation from a cavity mode that is responsible for the generation of low-frequency pulsating oscillations. We discuss the role of optothermal effects in the formation of the pulsed dynamics. Self-pulsing regimes in semiconductor lasers have been analyzed, experimentally and theoretically, for decades and continue to attract significant attention due to the strong impact of these instabilities on the laser performance and its applications [1]. The observation of pulsating intensity oscillations in the GHz range is conventionally attributed to saturable absorption (passive Q-switching). These selfsustained pulsations in bulk and quantum-well lasers are generated by the presence of saturable absorbing regions located outside the active region [2]. In order to explain the self-pulsations in quantum-dot (QD) lasers, the saturable absorption was assumed to be the result of inhomogeneous broadening of the gain and the existence of several confined QD states [3]. A recent experimental investigation of an InAs QD laser without a saturable absorber reported on large amplitude self-sustained pulsations in the MHz range [4]. The MHz range and the nonmonotonic change of the pulsation frequency with current exclude the passive Q-switching mechanism. The shape of each pulse corresponds to a sharp jump up, a slower decay, followed by a drop out. The slower decay is less pronounced at higher pumping currents. There is a jitter in the pulse width for the full range of pump currents. Due to limited information from the grower, we have no details on the material properties of the device, which operates strictly at the ground state (GS) transition.QD-based semiconductor lasers offer several advantages for applications such as a low-threshold current, temperature stability, and small dynamical chirp [5]. Of particular interest is a high damping rate of the relaxation oscillations (ROs) compared to the ROs of lasers based on bulk and QW materials [6,7]. This implies a higher stability with respect to optical feedback [8] and optical injection [9]. Lasers free of ROs are known as "Class A lasers" and approach their equilibrium exponentially like an overdamped oscillator. By contrast, lasers known as "Class B lasers" exhibit slowly decaying ROs toward their steady state. Only one equation for the amplitude of the field is needed for Class A lasers while we need both the equation for the field and the equations for the material variables in the case of Class B lasers.In this paper, we consider a mathematical model for a Class A laser that admits large amplitude self-sustained pulsations. The period of the oscillations is several orders larger than the laser cavity r...