Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links between these representations in terms of mathematical analysis but also in terms of modeling and numerical simulations. We illustrate this approach on the model of chemostat.

arXiv admin note: substantial text overlap with arXiv:1308.2411