Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism

We consider a stochastic chemostat model involving two obligate mutualistic species feeding on a limiting substrate. It is shown that the spatial arrangement of the random states near the deterministic coexistence equilibrium is enlarged as noise intensity increases. More precisely, in this paper, based on the technique of stochastic sensitivity functions, a confidence ellipse of the random states is constructed and a critical value for the noise intensity is established. It is shown that a new dynamic phenomenon of noise-induced extinction can be observed when the noise intensity passes the critical value. We then propose some feedback control strategies which can reduce the size of the confidence ellipse so that to prevent the noise-induced extinction.