A plausible physical explanation of a new advanced high-density H (HDH)-mode operational regime on the W7-AS stellarator is discussed. The HDH regime can be achieved only under a high rate of particle fueling during the starting phase of the discharge. It can be shown that at high enough fueling rates, the density profile grows at the source position, because the relatively weaker diffusivity hinders redistribution of the plasma. This leads to formation of a density gradient at the edge and brings about the radial electric field, which suppresses the plasma turbulence [the edge transport barrier (ETB) formation]. The appearance of the ETB depends on the initial condition, i.e., on the fueling rate, but a steady-state operation depends on the average density value. This critical value can be assessed from the energy and particle balance at the edge, where the transport coefficients depend on the plasma parameters in such a way that bifurcation can occur. The bifurcation occurs between two stable solutions, which are characterized by different values of the particle flux and energy confinement time, reminiscent of the normal confinement and HDH stages. The scaling analysis shows that the threshold average density required for transition increases weakly with power and inverse aspect ratio.