一类具有Crowley-Martin型的恒化器模型的定性分析

研究了恒化器中一类具有Crowley—Martin型功能反应函数的单种微生物培养系统,应用微分方程定性理论,得到微生物培养失败和成功的充分条件．最后给出本文的一个应用．     

一类相互干扰的捕食与被捕食种群模型的稳定性

本文运用常微分方程稳定性理论及方法讨论了一类具有相互干扰的捕食与被捕食模型的稳定性,得到了正平衡点的局部稳定性条件,正平衡点在第一象限的全局稳定性条件及解的有界性．     

具有常数输入及非线性发生率的SIQR传染病模型

讨论一类具有常数输入及非线性发生率的SIQR传染病模型,给出了疾病是否流行的阈值R₀=1.当R₀<1时,系统的唯一无病平衡点是全局渐近稳定的;当R₀>1时,系统有两个地方病平衡点,利用特征根法讨论了这两个地方病平衡点的稳定性,得出在某些参数范围内会出现Hopf分支现象;当R₀=1时,系统有唯一的地方病平衡点,利用中心流形定理证明了该地方病平衡点是不稳定的.     

一类具有垂直传染的SIR传染病模型

讨论了一类具有垂直传染的SIR传染病模型：(dS)/(dt)=6(1-m)(S R) (1- m)pb′I-βSI,(dI)/(dt)=βSI qb′I-d′I-rI,(dR)/(dt)=rI mb(S R) mpb′I-dR获得了无病平衡点与地方病平衡点的全局稳定性．     

一类具饱和传染力和常数输入的SIRS脉冲接种模型研究

利用Floquet乘子理论,研究了一类具饱和传染力和常数输入的SIRS脉冲接种模型,得到了无病周期解全局渐近稳定和系统持久的充分条件.     

一类具有饱和发生率的SEIS模型的全局稳定性

建立并分析了一类具有饱和发生率、在潜伏期具有传染性的SEIS模型.得到了模型的基本再生数R_0和无病平衡点与地方病平衡点全局渐近稳定的充分条件.     

一类具有非线性传染力的传染病模型的稳定性分析

研究了一类具有非线性发生率的急慢性阶段传染病模型,得到了确定模型全局动力性的阀值参数-基本再生数R_0,证明了R_01时,无病平衡点是全局渐近稳定的,疾病消失;若R_01,则存在地方病平衡点且是稳定结点,并证明了一定条件下地方病平衡点是全局渐近稳定的,疾病将蔓延.     

一类具有隔离干预的非线性传染率的传染病模型的全局稳定性分析(英文)

研究一类具有隔离干预的非线性传染率的SIQR传染病模型的全局稳定性,得到了阈值R及无病平衡点和地方病平衡点的存在的条件,并利用构造李雅普诺夫函数证明无病平衡点和地方病平衡点的全局稳定性.     

一类具有免疫反应的HollingⅡ型发生率病毒动力学模型

建立并讨论了一类具有潜伏期、抗体免疫反应和CTL免疫反应的Holling II型发生率病毒动力学模型.定义了决定这个模型动力学性质的五个阈值,借助适当的Lyapunov函数得到:当R_(01)≤1时,无病平衡点全局渐近稳定,病毒被清除;当R_(01)1,R_(02)≤1,R_(03)≤1时,无免疫平衡点全局渐近稳定;当R_(02)1,R_(04)≤1时,CTL免疫主导平衡点全局渐近稳定;当R_(03)〉1,R_(04)≤1时,抗体免疫主导平衡点全局渐近稳定;当R_(04)1,R′_(04)1时,正平衡点全局渐近稳定.     

一类具有常数迁入且总入口在变化的SIRI传染病模型的稳定性

讨论一类具有常数迁入率,染病类有病死且有效接触率依赖于总人数的SIRI传染病模型.给出了基本再生数σ的表达式.如果σ≤1,则疾病消除平衡点是全局稳定的;如果σ＞1,则存在唯一的传染病平衡点且是局部渐近稳定的.对具有双线性传染率和标准传染率的相应模型,进一步证明了当σ＞1时传染病平衡点的全局稳定性.     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.     

一类潜伏期和染病期均传染且具非线性传染率的流行病模型

研究了一类潜伏期和染病期都传染的具非线性传染率的SEIS流行病模型,确定了各类平衡点存在的条件阈值,讨论了各平衡点的稳定性,揭示了潜伏期传染和染病期传染对流行病发展趋势的共同影响．     

作物生长温度效应的非线性模型及其比较研究

通过严密的数学证明,发现了前人关于作物生长温度效应非线性模型之间的内在联系,修正了有关学者对模型参数定义的局限性,提出了一个通用的作物生长温度效应非线性模型,本研究还将该模型与笔者最近提出的基于高斯方程的非线性模型进行了比较研究,介绍了应用SAS软件求取两个模型相关参数的方法,并以马铃薯生育期模拟为例进行了实证研究,表明这两个模型均有良好的适用性。     

杂交瘤细胞培养中摄氧速率(OUR)的在线检测及其与细胞生长及代谢的关系

在批式及灌流培养条件下研究了杂交瘤细胞在无血清培养基中的生长、代谢情况与氧消耗的关系。应用动力学方法在线进行OUR的检测,同时离线取样检测其他参数。结果发现OUR与谷氨酰胺的消耗、抗体的生成及活细胞密度间有明显的相关关系,进一步的分析还发现在对数生长期,OUR与活细胞密度间具有良好的线性关系,qOUR(0.103±0.028)×10^-12mol/cell/h,可以通过它来进行细胞密度的在线检测。并通过以ΔOUR=0时刻作为灌流调整点进行连续灌流培养的初步实验验证了OUR作为培养过程反馈控制参数的可能性。     

A New Method for Calculating Net Reproductive Rate from Graph Reduction with Applications to the Control of Invasive Species

Matrix models are widely used for demographic analysis of age and stage structured biological populations. Dynamic properties of the model can be summarized by the net reproductive rate R ₀. In this paper, we introduce a new method to calculate and analyze the net reproductive rate directly from the life cycle graph of the matrix. We show, with examples, how our method of analysis of R ₀ can be used in the design of strategies for controlling invasive species.     

局部供磷对玉米根系生长、磷吸收速率的影响

玉米幼苗种子根局部供磷可明显改变根系的形态。供磷区侧根生长增加,无磷区侧极生长减少。供磷区1次、2次侧根长度与2次侧根数量明显增加;而1次侧根数量则不增加。供磷区缩小时,根系生长加快,单位根区磷吸收速率增加,但单位根重磷吸收速率的增加不很明显。磷局部供应植株主要通过供磷区根系的生长来增加磷的吸收,以满足植株对磷的需求。局部供磷植株中转运到供磷根区的光合产物明显多于无磷根区。     

一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型的周期解

研究了一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型．证明了无脉冲系统的负向全局渐近稳定性及带有脉冲状态反馈控制系统具有阶一周期解,并且给出阶一周期解存在和稳定的充分条件．数值模拟验证了理论结果．     

Substrate uptake tests and quantitative FISH show differences in kinetic growth of bulking and non-bulking activated sludge

The competition between filaments and floc formers in activated sludge has been historically described using kinetic selection. However, recent studies have suggested that bacterial storage may also be an important factor in microbial selection, since the dynamic nature of substrate flows into wastewater treatment plants elicit transient responses from microorganisms. Respirometry-based kinetic selection should thus be reevaluated by considering cell storage, and a more reliable method should be developed to include bacterial storage in the analysis of growth of filaments and floc formers in activated sludge. In this study, we applied substrate uptake tests combined with metabolic modeling to determine the growth rates, yields and maintenance coefficients of bulking and non-bulking activated sludge developed in lab scale reactors under feast and famine conditions. The results of quantitative fluorescence in situ hybridization (FISH) showed that the filaments Eikelboom Type 1851, Type 021N, and Thiothrix nivea were dominant in bulking sludge, comprising 42.0 % of mixed liquor volatile suspended solids (MLVSS), with 61.6% of the total filament length extending from flocs into bulk solution. Only low levels of Type 1851 filament length (4.9% of MLVSS) occurred in non-bulking sludge, 83.0% of which grew inside the flocs. The kinetic parameters determined from the substrate uptake tests were consistent with those from respirometry and showed that filamentous bulking sludge had lower growth rates and maintenance coefficients than non-bulking sludge. These results provide support for growth kinetic differences in explaining the competitive strategy of filamentous bacteria.     

Uptake Kinetics of 2,4-Dichlorophenoxyacetate by Delftia acidovorans MC1 and Derivative Strains: Complex Characteristics in Response to pH and Growth Substrate

The present investigation showed that active processes were involved in the uptake of 2,4-dichlorophenoxyacetate (2,4-D) by Delftia acidovorans MC1. With 2,4-D-grown cells, uptake at pH 6.8 was highly affine and showed a complex pattern-forming intermediary plateau at 20–100 μM 2,4-D. The kinetics became increasingly sigmoidal with raising of the pH to 7.5 and 8.5, and complexity disappeared. The apparent maximum was obtained at around 400 μM 2,4-D at either pH, and amounted to 15–20 nmol/min*mg protein. Higher substrate concentrations resulted in significant inhibition. With cells grown on (RS)-2-(2,4-dichlorophenoxy)propionate, 2,4-D uptake increased significantly and reached 45 nmol/min*mg, hinting at induction of a specific carrier(s). The kinetic characteristics made it apparent that several proteins contribute to 2,4-D uptake in MC1. An open reading frame was detected which has similarity to genes encoding major facilitator superfamily (MFS) transporters. Mutant strains that lacked this gene showed altered kinetics with decreased affinity to 2,4-D at pH 6.8. A mutant with complete deficiency in phenoxyalkanoate utilization showed an almost linear uptake pattern hinting at sole diffusion. Cloning of tfdK encoding a specific transporter for 2,4-D resulted in an increased uptake rate and, above all, higher affinity at slightly alkaline conditions due to hyperbolic kinetics. The presence of carbonylcyanide m-chlorophenylhydrazone led to the subsequent strong inhibition of 2,4-D uptake, suggesting proton symport as the likely active mechanism.     

Control of Leaf Growth and its Role in Determining Variation in Plant Growth Rate from an Ecological Perspective

Abstract: Plants vary widely in their relative growth rate (RGR), be it dependent on environmental conditions or due to their genetic background. In a comparison of the RGR of grasses growing under different environmental conditions, variation in RGR tends to correlate with that in the leaf elongation rate (LER). When different species or genotypes thereof are compared under identical growing conditions, variation in LER may or may not correlate with that in RGR, depending on the comparison. However, since RGR is described by an exponential equation, whereas LER is mainly a linear process, we conclude that any correlation between RGR and LER must be fortuitous. That is, exponential growth must be due to increases with time in plant traits such as 1) leaf dry mass per unit leaf length invested per unit time, and/or 2), i.e., the total LER of all the growing leaves at one point in time. The latter can be achieved as follows: 1) each subsequent leaf has a higher LER than the preceding one; 2) leaves appear at an increasing rate; 3) the duration of the process of leaf elongation increases for subsequent leaves. In this review, we only explore possible factors that account for changes in with time, in different genotypes and under different environmental conditions. Inherent variation in LER of individual leaves and variation due to environmental factors may reflect variation in the rate of cell division and/or in cell elongation.