具时滞的捕食与被捕食系统的动力分析

研究了具有时滞的捕食与被捕食系统,分析了系统的正不变集、边界平衡点性质、全局渐近稳定性和持久生存性.当时滞(?)很小时,系统在正平衡点是局部渐近稳定的,当(?)从0增到(?)_0时,系统在正平衡点附近产生Hopf分支.     

KOLMOGOROV模型的无害时滞

1．引言考虑具有时滞的两种群相互作用模型的稳定性。其中τ_ij∈〔0,∞）,i,j=1,2．f和g对所含变元连续。假设存在正常数平衡点（x~*,y~*）,x~*＞0,y`*＞0,使得f（x~*,y~*)=g（x~*,y~*）＝0．系统（1）的特别情形是（1）中当τ_ij=0时得到著名的Kolmogorov模型。定义⑴系统（1"'）具有一类型的时滞,如果个时滞无论大小如何都不改变系统（1"）的平衡位置（x~*,y`*）的渐近稳定性,则称此时滞为无害时滞。文献〔1〕-〔3〕得到系统（1'）类型的时滞为无害时滞的充分条件。文献〔2〕提出这样一个有趣的问题：系统（1）类型的时滞…     

捕食者有病的生态-流行病模型的分析

建立并分析了捕食者具有疾病且有功能反应的生态-流行病(SI)模型,讨论了解的有界性．应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。     

具有Crowley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性（英文）

本文讨论了一类具有Growley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性.利用Lyapunov函数和LaSalle不变原理证明:当基本再生数R_0≤1时,无病平衡点全局渐近稳定;当基本再生数R_01且免疫基本再生数R_0≤1时,免疫平衡点全局渐近稳定;当R_01时,地方病平衡点全局渐近稳定.     

一类基于比率且具双线性密度制约的捕食-食饵系统的全局稳定性分析

研究一类基于比率和具双线性密度制约的捕食-食饵系统．由Bendixson环域定理及比较定理给出了奇点（0,0）和（1,0）全局渐近稳定的条件．通过对等倾线的研究给出了正平衡点存在的条件,并构造了Dulac函数讨论其全局渐近稳定性．     

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.     

具有三个年龄阶段的单种群自食模型

建立并研究了两个具有三个年龄阶段的单种群自食模型．这篇文章的主要目的是研究时滞对种群生长的作用,对于没有时滞的的模型,我们利用Liapunov函数,得到了系统平衡点全局渐近稳定的充分条件;而具有时滞的的模型,我们得到,随着时滞T增加,当系数满足一定条件时,正平衡点的稳定性可以改变有限次,最后变成不稳定;否则,时滞模型的正平衡点的稳定性不改变。     

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.     

食饵有病的生态-流行病模型的稳定性研究

在考虑捕食者捕食染病的食饵对自身的不利作用的基础上建立了食饵有病的生态-流行病模型,得到了系统平衡点局部渐近稳定的充分条件;讨论了系统的非负不变性、解的有界性,并在此基础上研究了边界平衡点的全局稳定性,得到了平衡点全局稳定的充分条件。     

分数阶SIR传染病模型的稳定性分析（英文）

本文研究一类Caputo型分数阶SIR传染病模型的全局稳定性.首先,通过对方程进行求解得到了模型的平衡点.然后,根据关于Caputo型分数阶微积分的一个引理和分数阶动力系统的相关理论,分别构造相应的Lyapunov函数判断平衡点的稳定性.结果表明,当R_01时,模型有唯一的无病平衡点E_0,E_0是全局稳定的;如果R_01时,模型存在无病平衡点E_0和地方病平衡点E_*,E_*是全局稳定的.最后,给出了一些数值模拟来验证理论分析的结果.     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

一类被开发的捕食系统的定性分析

讨论了一类食饵种群被开发的两种群捕食系统: dx/dt=x(a0+a1x-a2x2-a3y3)-h0, dy/dt=y(x-1)其中a0>0,a2>0,a3>0,h0>0,a1不定号.文中主要讨论了系统平衡点的行为以及系统的稳定性.用Pioncare切性曲线法及Dulac函数法讨论闭轨不存在的充分条件;用Hopf分支方法及张芷芬唯一性定理证明了极限环的存在性与唯一性.同时对相应结论的生态学意义给予了说明.     

Spatial Distribution of the Potential on a Cylindrical Surface Simulating the Somatic Membrane: Model Studies

In our study, we represent the theoretical and numerical analysis of a stochastic version of the Hodgkin–Huxley model applied to a two-dimensional spatial cylindrical area simulating the neuronal somatic membrane. We characterized the spatiotemporal dynamics of the membrane potential by its local value V _m (x, y, t) and the integral of this value with respect to time F(x, y, T) within an interval [0, T]. Analysis of the model showed that (i) there are nonzero gradients of F(x, y, T) at any distribution of ion channels; (ii) the maximum gradient F(x, y, T) decreases down to zero with the time T, if the channels are distributed homogeneously, and acquire some positive constant value, if the channels are distributed inhomogeneously; the gradient F(x, y, T) depends on the gradient of spatial distribution of the channels; and (iii) under conditions of spatial redistribution of the channels with preservation of their number, the dynamics of V _m (x, y, t) does not change.     

Dynamic analysis of lactic acid fermentation in membrane bioreactor

In this paper, a mathematical model for the lactic acid fermentation in membrane bioreactor is investigated. This novel theoretical framework could result in an objective criterion on how to control the substrate concentration in order to keep a sustainable and steady output of lactic acid. Firstly, continuous input substrate is taken. The existence and local stability of two equilibria are studied. According to Poincaré-Bendixson Theorem, we obtain the conditions for the globally asymptotical stability of the equilibrium. Secondly, impulsive input substrate is also considered. Using Floquet's theorem and small-amplitude perturbation, we obtain the biomass-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations.     

Chemical modification results in hyperactivation and thermostabilization of Fusarium solani glucoamylase

Chemical modification of carboxyl groups of glucoamylase from a mesophilic fungus, Fusarium solani, was carried out using ethylenediamine as nucleophile in the presence of water-soluble 1-ethyl-3(3-dimethylaminopropyl)carbodiimide. Modification brought about a dramatic enhancement of catalytic activity and thermal stability of glucoamylase. Temperature and pH optima of ethylenediamine-coupled glucoamylase (ECG) increased as compared with those of native enzyme. The specificity constant (k(cat)/K(m)) of native, ECG-2, ECG-11, and ECG-17 was 136, 173, 225, and 170, respectively, at 55 degrees C. The enthalpy of activation (Delta H*) and free energy of activation (Delta G*) for soluble starch hydrolysis were lower for the chemically modified forms. All of the modified forms were stable at higher temperatures and possessed high Delta G* against thermal unfolding. The effects of alpha-chymotrypsin and subtilisin on the modified forms were activating as compared with native. Moreover, denaturation of ECG-2, ECG-11, and ECG-17 in urea at 4 mol x L(-1) also showed an activation trend. A possible explanation for the thermal denaturation of native and increased thermal stability of ECG-2, ECG-11, and ECG-17 at higher temperatures is also discussed.     

Alternative stable equilibria and critical thresholds created by fire regimes and plant responses in a fire‐prone community

Wildfire is a dominant disturbance in many ecosystems, and fire frequency and intensity are being altered as climates change. Through effects on mortality and regeneration, fire affects plant community composition, species richness, and carbon cycling. In some regions, changes to fire regimes could result in critical, non‐reversible transitions from forest to non‐forested states. For example, the Klamath ecoregion (northwest United States) supports extensive conifer forests that are initially replaced by hardwood chaparral following high‐severity fire, but eventually return to conifer forest during the fire‐free periods. Climate change alters both the fire regime and post‐fire recovery dynamics, potentially causing shrubland to persist as a stable (i.e. self‐renewing) vegetation stage, rather than an ephemeral stage. Here, we present a theoretical investigation of how changes in plant traits and fire regimes can alter the stability of communities in forest‐shrub systems such as the Klamath. Our model captures the key characteristics of the system, including life‐stage‐specific responses to disturbance and asymmetrical competitive interactions. We assess vegetation stability via invasion analysis, and conclude that portions of the landscape that are currently forested also can be stable as shrubland. We identify parameter thresholds where community equilibria change from stable to unstable, and show how these thresholds may shift in response to changes in life‐history or environmental parameters. For instance, conifer maturation rates are expected to decrease as aridity increases under climate change, and our model shows that this reduction decreases the fire frequencies at which forests become unstable. Increases in fire activity sufficient to destabilize forest communities are likely to occur in more arid future climates. If widespread, this would result in reduced carbon stocks and a positive feedback to climate change. Changes in stability may be altered by management practices.     

相岭山系冕宁冶勒自然保护区大熊猫-竹子种群数学模型的研究

本文对袁重桂、张洪德(1990)提出的大熊猫-竹子种群的数学模型做了较大的改进,加入了修正项(m-x2)y2/km得到新模型x=rx-ix-αx2-cy,y=by-dy-ey2-(m-x)y2/km其中的生命系数是作者在冕宁县冶勒自然保护区作实际资料收集统计得来的;并将α作为参数,当改变参数α时,正平衡点B是稳定的焦点或是不稳定的焦点;分支值α0存在于一个很小的区间,模型的相图的基本结构发生了较大的变化,出现了一个稳定的极限环。     

旱地施有机肥对土壤有机质和水稳性团聚体的影响

通过渭北旱塬2007-2010年田间定位试验,研究了有机肥不同施用量(低量7500 kg·hm^-2、中量15000 kg·hm^-2、高量22500 kg·hm^-2)对连作玉米地土壤有机质、团聚体各层粒径分布和稳定性的影响.结果表明：0～20 cm土层,高量有机肥处理土壤有机质含量较低量有机肥处理提高4.1%～4.6%,高、中量有机肥处理较对照提高4.6%～11.2%,低量有机肥处理在施肥第4年（2010年）较CK提高4.7%～6.3%.0～30 cm土层,所有有机肥处理>5 mm水稳性团聚体的增幅最大,其含量随有机肥用量的增加而显著升高;有机肥处理显著提高了土壤>0.25 mm水稳性团聚体含量、团聚体平均质量直径和团聚体稳定率,且随有机肥用量的增加而显著增加;中、高量有机肥处理比单施化肥处理增加效果显著.     

一类具功能反应的食饵-捕食者两种群模型的定性分析

研究了具功能反应的食饵-捕食者两种群模型：x=xg(x)-yф(x),y=y(-d eф(x))。在g(x)和ф(x)都是非线性情形下,讨论了该系统的平衡点的性态,并证明了极限环的存在性与唯一性及其全局稳定性。