Stochastic Sensitivity Analysis for a Competitive Turbidostat Model with Inhibitory Nutrients

Abstract

A stochastic model of turbidostat in which two microorganism species compete for an inhibitory growth-limiting nutrient is considered. In the deterministic case, the model has rich dynamics: a coexistence equilibrium and the washout equilibrium can be simultaneously stable, and a stable limit cycle may exist. In the stochastic case, a phenomenon of noise-induced extinction occurs. Namely, the stochastic trajectory near the deterministic coexistence equilibrium will tend to the washout equilibrium. Based on the stochastic sensitivity function technique, in this paper, we construct the confidence ellipse and then estimate the critical value of the intensity for noise generating a transition from coexistence to extinction. We also construct the confidence band to find the configurational arrangement of the stochastic cycle.