Dynamical behavior of a stochastic food chain chemostat model with Monod response functions

This paper studies a food chain chemostat model with Monod response functions, which is perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. Moreover, we consider the extinction of microbes in two cases. In the first case, both the predator and prey species are extinct. In the second case, only the predator species is extinct, and the prey species survives. Finally, numerical simulations are carried out to illustrate the theoretical results.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

Steady-state solutions of a reaction–diffusion system arising from intraguild predation and internal storage

Intraguild predation is added to a mathematical model of competition between two species for a single nutrient with internal storage in the unstirred chemostat. At first, we established the sharp a priori estimates for nonnegative solutions of the system, which assure that all of nonnegative solutions belong to a special cone. The selection of this special cone enables us to apply the topological fixed point theorems in cones to establish the existence of positive solutions. Secondly, existence for positive steady state solutions of intraguild prey and intraguild predator is established in terms of the principal eigenvalues of associated nonlinear eigenvalue problems by means of the degree theory in the special cone. It turns out that positive steady state solutions exist when the associated principal eigenvalues are both negative or both positive.     

The existence of stationary distribution of a stochastic delayed chemostat model

In this paper, based on the existing literature, we further study an important statistical character of a stochastic delayed chemostat model. By constructing suitable Lyapunov functional and using the stochastic Lyapunov analysis method, we investigate the existence of stationary distribution and the ergodicity of a stochastic delayed chemostat model, which can help us better understand the dynamic behavior and statistical characteristics of stochastic delayed biological models.     

Continuous hydrogen photoproduction by Chlamydomonas reinhardtii

This study demonstrates, for the first time, that it is possible to couple sulfate-limited Chlamydomonas reinhardtii growth to continuous H₂ photoproduction for more than 4000 h. A two-stage chemostat system physically separates photosynthetic growth from H₂ production, and it incorporates two automated photobioreactors (PhBRs). In the first PhBR, the algal cultures are grown aerobically in chemostat mode under limited sulfate to obtain photosynthetically competent cells. Active cells are then continuously delivered to the second PhBR, where H₂ production occurs under anaerobic conditions. The dependence of the H₂ production rate on sulfate concentration in the medium, dilution rates in the PhBRs, and incident light intensity is reported.     

Analysis of Monod type food chain chemostat with k-times’ periodically pulsed input

In this paper, we introduce and study a model of a predator-prey system with Monod type functional response under periodic pulsed chemostat conditions, which contains with predator, prey, and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.     

Continuous production of mixed alcohols and acids from carbon monoxide

Continuous, steady-state fermentations using carbon monoxide gas as the sole carbon and energy source have been achieved with the CO strain ofButyribacterium methylotrophicum. Fermentation pH was found to regulate carbon monoxide metabolism over the pH range of 6.8 to 5.0. Cell growth diminished at low pH, with washout occurring at pH 5.0. As observed previously in batch culture, lower pH values favored production of butyrate over acetate. The mechanism responsible for this trend is currently being investigated by quantification of key intracellular enzyme activities. At low pH values, direct, steady-state fermentation of carbon monoxide to alcohols has been verified. Of major significance is the production of butanol from carbon monoxide in pure culture. This newly identified pathway provides a potential mechanism for direct bioconversion of synthesis gas to butanol.     

A mathematical model of ethanol fermentation from cheese whey

The cybernetic approach to modeling of microbial kinetics in a mixedsubstrate environment has been used in this work for the fermentative production of ethanol from cheese whey. In this system, the cells grow on multiple substrates and generate metabolic energy during product formation. This article deals with the development of a mathematical model in which the concept of cell maintenance was modified in light of the specific nature of product formation. Continuous culture data for anaerobic production of ethanol byKluyveromyces marxianus CBS 397 on glucose and lactose were used to estimate the kinetic parameters for subsequent use in predicting the behavior of microbial growth and product formation in new situations.