Dynamical Analysis of a Stochastic Chemostat Predator-Prey Model with Impulsive Toxicant Input

This paper investigates the dynamics of a predator-prey chemostat model in a polluted environment, incorporating both impulsive toxicant input and stochastic environmental noise. Deterministic and stochastic formulations with a Monod-type functional response are developed, and sufficient conditions for microbial extinction and persistence are established analytically. For the deterministic impulsive system, we derive explicit criteria for the global stability of the microbial extinction periodic solution, predator extinction with prey survival, and predator-prey coexistence. When stochastic perturbations affect the maximum growth rate, we obtain extinction and persistence thresholds in the mean sense and further prove the existence of a unique ergodic stationary distribution for systems subject to nonlinear higher-order perturbations. Numerical simulations confirm the theoretical findings and illustrate the joint inhibitory effects of pulsed toxicants and environmental noise on microbial culture. Results indicate that stochastic disturbances generally suppress microbial persistence, while increased toxicant input further reduces microbial concentrations, highlighting the challenges in sustaining microbial populations under combined pollutant and stochastic stress.