Stationary distribution of a stochastic food chain chemostat model with general response functions

In this paper, we focus on a food chain chemostat model with general response functions, perturbed by white noise. Under appropriate assumptions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution by using stochastic Lyapunov analysis method. Our main effort is to construct the suitable Lyapunov function.     

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

In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.     

自全国各地100多位理事Road Machinery Branch of China Highway and Transportation Society He

In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.     

Bifurcation in the stable manifold of a chemostat with general polynomial yields

A three‐dimensional chemostat with nth‐ and mth‐order polynomial yields, instead of the particular ones such as A+BS, A+BS², A+BS³, A+BS⁴, A+BS² + CS³, and A+BSⁿ, is proposed. The existence of limit cycles in the two‐dimensional stable manifold, the Hopf bifurcation, and the stability of the periodic solution created by the bifurcation is proved. Copyright © 2009 John Wiley & Sons, Ltd.     

Development of Methods to Measure Carbon Isotope Ratios of Bacterial Biomarkers in the Environment

Abstract

The δ¹³C value of bacterial carbon is an important parameter in microbial ecology for studying the carbon flow within a microbial community and for the identification of ecological important strains involved in the mineralization of certain carbon pools in the environment. In our study, biomarkers were isolated from bacteria from a microbial consortium derived from two chemostats and δ¹³C values were measured. Similar isotope ratios between biomarkers such as fatty acids and outer membrane protein, biomass and substrate were observed. The δ¹³C analyses of outer membrane protein F of Pseudomonas and biomarker fatty acids were combined to follow bacterial assimilation of ¹³C labelled 4-chlorocatechol. This new approach was also used in the environment where soil samples were cultivated with different ¹³C traced substrates.

The isotopic analyses of bacterial biomarkers indicated that carbons of histidine were widely incorporated into bacterial biomarkers, in contrast to 4-chlorocatechol which was less often used as a substrate. Results indicate that by isolating bacterial biomarkers and measuring their δ¹³C values, activities of microbial communities in a complex environmental sample can be determined. This new method has the potential to elucidate individual carbon sources for individual bacterial taxa in microbial ecology.     

Study of a Monod–Haldene type food chain chemostat with pulsed substrate

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with 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.     

改进的口腔微生物种群模型及其Lyapunov稳定性

考察人体口腔异味现象,利用恒化器建模方法,改进了人体口腔系统中微生物种群关系的模型,利用Lyapunov稳定性理论分析了系统的平衡点及其稳定性.进而得到结论,口腔异味作为疾病,需要专业医治才能治愈.数值模拟结果证实了理论分析的正确性.     

带有再生养分流的海洋生物群落的生长模型及其渐近性态

本文建立了具有一般养分吸收功能的多种海洋生物种群的生长模型,各种群为了争夺共同的资源而竞争,外界资源供给增量是时间的有界函数,一般地带有滞后的再生养分流补充,并且考虑各种群间竞争因素和每个种群内部的干扰因素。该文讨论了模型的有界性,并证明了当干扰常数m<1时,所考虑的生物群落是永久持续生存的,即每个种群都有正的上下限,当m=1时,在再生养分无滞后时建立了若干种群灭绝的充分条件和持续生存的必要条件。     

具有双参数的培养器系统的Hopf分支

We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.     

BIFURCATION AND COMPLEXITY IN A RATIO-DEPENDENT PREDATOR-PREY CHEMOSTAT WITH PULSED INPUT

In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution （xs（t）, O, zs（t）） is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period T the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.