Stationary probability density of a stochastic chemostat model with Monod growth response function

Abstract

The stationary probability density (SPD) is derived and studied for a stochastic chemostat model with Monod growth response function. First, with the help of polar coordinate transformation and stochastic averaging method, we derive a two‐dimensional diffusion process of averaged amplitude and phase angle. Furthermore, the SPD of the diffusion process is obtained by the corresponding Fokker Planck‐Kolmogorov equation. We also analyze the effects of noise intensities on the geometric property of the SPD.