Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

Abstract

A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.

Theoretical and conceptual derivation of threshold phenomena and metabolic switching models in a chemostat system

“…These systems have been used for many applications including low-cost cultures such as yeast (Matteau et al, 2015;Payen and Dunham, 2017), biological evolution analysis (Gresham and Hong, 2015), microbial systems (Ziv et al, 2013), etc. More sophisticated models such as that of Zhang et al (2017), Rapaport et al (2018), etc., have also been developed.…”

“…To meet this situation, the "modelbuilder" must introduce some conditional tests in his or her algorithm and choose the option that best corresponds to the "pre-established" optimization criterion. Growth on multiple substrates, also known as diauxie, is one of the main phenomena that led to this kind of modeling (Zhang et al, 2017). The problem that arises is then to represent the "switch" correctly that allows for the consumption of a second, less "favored" substrate after the exhaustion of the first substrate.…”

Stationary distribution and extinction for a food chain chemostat model with random perturbation

“…It is crucial and essential to study the effect of stochastic disturbance on the continuous culture of microbes. On the one hand, some authors have investigated the chemostat systems with parameters perturbation (see, e.g., the literature [15][16][17][18][19][20]. In the paper by Sun et al, 19 the asymptotic behavior of a stochastic Lotka-Volterra food chain chemostat model was studied, where they introduced the randomness on the dilution rate.…”

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

“…However, some experiments show that the growth of a microorganism depends on a variety of nutrition factors such as carbon, nitrogen, energy, growth factors, inorganic salts, and water [19]. Recently, the growth of microorganism species in the chemostat on continuous multi-nutrient has been investigated by many researchers [20][21][22][23]. While the species in nature are subject to short-term interference (for example, seasonal harvest, natural enemies, spraying pesticides, etc.…”