Long-time behavior of a perturbed enzymatic reaction model under negative feedback process by white noise.

In this paper, we will discuss a stochastic enzymatic reaction model under negative feedback process. We will prove that the solution of the system is positive and global. Furthermore, we draw a conclusion that there is a stationary distribution for the stochastic system and it has ergodicity without any additional conditions. Finally, we test our theory conclusion by simulations. It is interesting that our stochastic model is always ergodic. [ABSTRACT FROM AUTHOR]