Noise-induced bifurcations in the stochastic chemostat model with general nutrient uptake functions

Abstract

This paper mainly focuses on studying the noise-induced bifurcation in the stochastic chemostat model with general nutrient uptake functions. The dynamic behavior of the chemostat is classified by using the Feller test method, and the stationary distribution is obtained in a closed form. Based on the stationary distribution, we show that the solution almost surely goes around the deterministic equilibrium point when the noise is small. Using the noise intensity as a bifurcation parameter, it is proven that the model undergoes a dynamical (D) bifurcation and a phenomenological (P) bifurcation. Computer simulations illustrate the bifurcation phenomena for several chemostats with different types of nutrient uptake functions.