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.