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Statistical property analysis for a stochastic chemostat model with degenerate diffusion

By considering the fact that the growth of microorganisms in a chemostat is subject to white noise, we construct a stochastic chemostat model with degenerate diffusion by using a discrete Markov chain. By solving the corresponding Fokker-Planck equation, we derive the explicit expression of the stationary joint probability density, which peaks near the deterministic equilibrium. Next, we simulate the the marginal probability density functions for different noise intensities and further discuss the relationship of the marginal probability density function and noise intensities. For the statistical properties of the stochastic model, we mainly investigate the effect of white noise on the variance and skewness of the concentration of microorganisms.