  We study theoretically nonlinear valley polarization dynamics of excitons in
atom-thin semiconductors. The presence of significant polarization slows down
valley relaxation due to an effective magnetic field resulting from
exciton-exciton interactions. We address temporal dynamics of valley polarized
excitons and study the steady states of the polarized exciton gas. We
demonstrate bistability of the valley polarization where two steady states with
low and high valley polarization are formed. We study the effects of
fluctuations and noise in such system. We evaluate valley polarization
autocorrelation functions and demonstrate that for a high-polarization regime
the fluctuations are characterized by high amplitude and long relaxation time.
We study the switching between the low- and high-valley polarized states caused
by the noise in the system and demonstrate that the state with high valley
polarization is preferential in a wide range of pumping rates.
