Stability and bifurcation of stochastic chemostat model

The main purpose of this paper is to study dynamics of stochastic chemostat model. In this order, Taylor expansions, polar coordinate transformation and stochastic averaging method are our main tools. The stability and bifurcation of the stochastic chemostat model are considered. Some theorems provide sufficient conditions to investigate  stochastic stability, $D$-bifurcation and $P$-bifurcation of the  model. As a final point, to show the effects of the  noise intensity and illustrate our theoretical results, some numerical simulations are presented.