| Abstract: |
| In this talk, we consider the so-called deterministic anaerobic digestion model number 2, derive its stochastic version by perturbing the maximal growth rate of acidogenic microorganisms with a white noise, and investigate the global dynamics of the stochastic model obtained. By mainly relying on $It\hat{o}$ formula, combined with other tools from stochastic analysis, we first prove the existence and uniqueness of a global positive strong solution of the stochastic model. Then, we explore and derive the conditions of persistence and extinction of the microorganisms. Finally, by performing some numerical simulations, we illustrate the theoretical results obtained. In some cases, the interpretation of the results enables clarification of conditions under which biogas can be produced. |
|