The dependence of the structure and stability of strongly asymmetric stationary states of a superradiant laser with a slightly asymmetric low-Q Fabry-Perot cavity on its length, reflection factors of mirrors, and pumping level is studied. The states are related to a self-consistent inhomogeneous half-wavelength population inversion grating. The possibility of the existence of two dynamic phase transitions from a stationary (monochromatic) state of this type to a nonstationary one is established: 1) a dissipative superradiant transition to a regime with a quasi-continuous lasing spectrum (in a weakly asymmetric cavity) and 2) a self-modulation transition to a regime with a discrete lasing spectrum. It is shown that the latter can be caused by excitation of both polariton and electromagnetic laser modes due to resonant Rabi oscillations of active centers with a sufficiently long phase relaxation time.