Steady state properties of a kinetic model of Smolen- Baxter- Byrne [P. Smolen, D. A. Baxter, J. H. Byrne, Amer. J. Physiol. Cell. Physiol. 274, 531 (1998)] are investigated in presence of two time- correlated noises. The steady state probability distribution can be obtained by solving the Fokker- Planck equation. It is found that both the correlated- time between the white noise and the colored noise and that between the colored noises can convert the bistability to monostability while the former activates the transcription and the latter suppresses it.

We use the logistic growth model to describe the bacterium growth in the presence of a Gaussian colored noise. The effects of multiplicative colored noise on the steady state probability distribution of the bacterium growth were investigated. Our results show that increasing the strength of the multiplicative colored noise may lead to decreasing bacterium number and even bacterium extinction. Our studies also indicate that increasing the correlate time of the noise may facilitate the bacterium growth to some extent.