Dynamics of the stochastic chemostat with Monod-Haldane response function

Area of Science:

• * Mathematical modeling
• * Microbial ecology
• * Stochastic processes

Background:

• * The chemostat model is a standard tool for studying microbial population dynamics.
• * Environmental fluctuations can significantly alter microbial behavior and survival.
• * Understanding the impact of noise is crucial for predicting population persistence.

Purpose of the Study:

• * To analyze a stochastic chemostat model with Monod-Haldane kinetics under environmental white noise.
• * To investigate the conditions for the existence of a stationary distribution and ergodicity.
• * To establish criteria for microbial population extinction and survival based on noise intensity.

Main Methods:

• * Application of Khasminskii's theory on ergodicity to analyze the stochastic model.
• * Development of sufficient criteria for population extinction.
• * Theoretical analysis complemented by numerical simulations.

Main Results:

• * The stochastic chemostat model with Monod-Haldane response possesses a global positive solution.
• * Conditions for the existence of a stationary distribution and ergodicity were established.
• * Noise intensity was found to be a critical factor: small white noise promotes survival, whereas large noise leads to extinction.

Conclusions:

• * Environmental white noise has a dual effect on microbial populations in the chemostat model.
• * The intensity of stochastic perturbations is a key determinant of population persistence or extinction.
• * Theoretical findings are supported by numerical simulations, offering insights into microbial ecosystem stability.