The behavior of the three-level single-mode laser in the presence of an applied field and a saturable absorber is revealed near the losing -threshold. It is shown by quantitatively calculating that nonlinearity of laser field and introduction of applied field cause the correspondence of steady states of the laser with the canonical cusp catastrophe manifold. In this paper the physical meaning of the cusp catastrophe manifold is explained in more detail. The quantitative condition for optical bistability generation is given.