Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion.

This paper considers a stochastic chemostat model with degenerate diffusion. Firstly, the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution. The authors show that the densities of the distributions of the solutions can converge in L¹ to an invariant density. Then, conditions are obtained to guarantee the washout of the microorganism. Furthermore, through solving the corresponding Fokker-Planck equation, the authors give the exact expression of density function around the positive equilibrium of deterministic system. Finally, numerical simulations are performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]