Competitive exclusion and coexistence in a general two-species stochastic chemostat model with Markov switching

In this paper, a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment. The model incorporates both white noise and telegraph noise, the latter being described by Markov process. The existence of a unique global positive solution for the stochastic chemostat model is established. Subsequently, by using the ergodic theory of Markov process and utilizing techniques of stochastic analysis, the critical value differentiating between persistence in mean and extinction for the microorganism species is explored. Moreover, the existence of a unique stationary distribution is proved by using stochastic Lyapunov analysis. Finally, numerical simulations are introduced to support the obtained results.