带有食饵保护的Holling-Ⅲ型扩散捕食系统的稳定性分析

本文研究了一类具食饵保护的Holling-Ⅲ型扩散捕食系统,带有齐次Neumann边界条件.首先,讨论了系统的全局吸引性;其次,给出了系统正常数平衡态局部/全局渐近稳定的充分条件,这些条件依赖于食饵保护参数;特别地,获得了扩散对系统常数平衡态稳定性的影响,即当扩散系数较大时可使得常数平衡态不稳定.     

一类具时滞和收获的捕食模型的稳定性与Hopf分支

本文研究一类具有常数收获率和时滞的捕食模型,其中时滞描述了捕食种群的妊娠期。通过分析特征方程,得到了正平衡点局部稳定的条件。当时滞τ增加时,正平衡点失去稳定性,当τ跨过临界值时系统将出现Hopf分支。应用中心流形定理和规范型理论,得到了确定Hopf分支方向和分支周期解的稳定性的计算公式。最后对所得理论结果进行了数值模拟。     

具有恐惧效应和狩猎合作的反应扩散模型的定性分析

研究了一类具有恐惧因子和狩猎合作的捕食–食饵反应扩散模型，以此探讨恐惧因子和狩猎合作对捕食系统动力学性质的影响。通过分析正平衡点的特征方程，得到了平衡点的局部渐近稳定性。结果表明，若不考虑恐惧因子，以狩猎合作系数α作为分支参数，得到Hopf分支点α*。当合作系数大于α*时，将恐惧因子e作为分支参数，得到Hopf分支点e*，在Hopf分支点附近会产生空间齐次和非齐次的周期解。另外，讨论了由扩散引起Turing失稳的条件，结果表明，当捕食者与食饵扩散率之比较小时，系统存在空间非均匀稳态解。这些结论能为如何维持生态平衡提供理论依据，最后利用数值模拟验证所得结论。     

具有一般传染率的 SIRS 年龄结构模型的分支研究

考虑到年龄在一些传染病流行过程中的重要影响,建立了一个具有一般传染率的 SIRS 年龄结构仓室模型。通过将模型改写为抽象柯西问题并利用 Hille-Yosida 算子相关定理,分析了模型的动力学性态,讨论了平衡点的稳定性以及平衡点失稳时产生 Hopf 分支的条件。结果表明,当基本再生数小于 1 时,免疫年龄不影响无病平衡点的全局稳定性;当基本再生数大于 1 时,免疫年龄扰动导致地方病平衡点的稳定性改变,从而产生 Hopf 分支。同时,数值模拟验证了理论结果并显示了免疫年龄对模型动力学性态的影响。     

超音速流中结构非线性二元机翼的复杂响应研究

基于活塞理论计算作用在二元机翼上的气动力，采用拉格朗日方程建立系统的运动微分方程。通过平衡点的Jacobi矩阵的特征方程求出了系统的Hopf分叉点，研究了带有立方非线性俯仰刚度二自由度机翼系统在典型参数下的稳定极限环颤振和混沌响应。结果表明，在超过一定的流体速度后，系统平衡点的个数及稳定性均发生了变化；随着流速的增大，在积分初始值较小时，系统出现混沌等极为复杂的响应。     

摆线钢球行星传动系统参数振动特性研究

摆线钢球行星传动系统为多自由度的参数振动系统,其时变啮合刚度激励会对系统的动态特性产生较大影响。该文首先综合考虑时变啮合刚度及轴承支承刚度等影响因素,建立了摆线钢球行星传动系统的平移-扭转耦合动力学模型,并推导出系统的动力学方程。然后将动力学方程转换为正则模态方程,并利用多尺度法对系统进行动力稳定性分析,推导出系统的组合共振频率及稳定性条件。最后利用摄动法计算出系统的稳态响应。研究结果表明:当偏心轴的输入转速接近和型组合共振频率时,系统将发生参数共振;当偏心轴的输入转速接近差型组合共振频率时,系统总是稳定的;系统的稳态响应中包含多种组合频率成分,并表现出多频响应叠加的特性。     

摆线钢球行星传动运动分叉特性研究

为揭示摆线钢球行星传动的非线性动力学行为,建立包括外部激励、啮合副啮合状态及啮合刚度等非线性因素的纯扭转强非线性耦合动力学模型。建立能够描述啮合副所处状态的预紧非线性函数,根据静力学分析获得啮合点静态变形量,建立非线性动力学微分方程组,利用数值分析方法获得系统随压缩量、阻尼系数变化的分叉图,并绘制不同参数下的相图和庞加莱图,研究不同参数对系统分叉特性的影响规律。结果表明:轴向压缩量对系统稳定性影响较大;轴向压缩量和旋转阻尼系数增加,高速运转的系统最终稳定于短周期运动,低速运转的系统最终稳定于准周期运动;阻尼较小时系统在低速状态下的稳定性较高,阻尼较大时系统在高速状态下的稳定性较高。     

具有三物种的食饵-捕食反应扩散时滞系统的稳定性与行波解

本文研究了在有界区域上带有Neumann边界条件的反应扩散三物种食饵-捕食时滞系统.利用特征值方法和Lyapunov函数找到了该系统平衡点稳定的充分条件,该条件说明时滞限制了稳定性.稳定性中的主要一个结论是当食饵和捕食者间的种内竞争大于种间竞争时正平衡点是全局渐近稳定的.进一步,通过构建上下解证明了当波速相对大时该系统具有连接零平衡点和正平衡点的行波解.     

具有三物种的食饵-捕食反应扩散时滞系统的稳定性与行波解（英文）

本文研究了在有界区域上带有Neumann边界条件的反应扩散三物种食饵-捕食时滞系统.利用特征值方法和Lyapunov函数找到了该系统平衡点稳定的充分条件,该条件说明时滞限制了稳定性.稳定性中的主要一个结论是当食饵和捕食者间的种内竞争大于种间竞争时正平衡点是全局渐近稳定的.进一步,通过构建上下解证明了当波速相对大时该系统具有连接零平衡点和正平衡点的行波解.     

带常数输入率TB模型的全局稳定性

研究了各分类均具有常数输入率先的一个TB模型的全局稳定性。根据广义的Bendixson判据，证明了当输入中含有受感染者时，模型不存在无病平衡点而具有唯一的地方病平衡点。当感染者的治愈率较小时，证明了该平衡点的全局渐近稳定性。     

一类捕食——食饵模型正解的存在唯一性与稳定性

本文主要研究一类具有非单调生长率的捕食食饵模型的平衡态正解问题．首先通过计算锥上紧算子的不动点指标,得到了正解存在的充分条件;其次,运用线性算子扰动理论以及拓扑度理论,讨论了参数对于正解唯一性与线性稳定性的影响;最后,通过数值模拟分别验证了在一维空间和二维空间下正解的存在性结论,也就是捕食者和食饵在一定条件下可以共存．     

Effect of cross diffusion on double diffusive convection in the presence of horizontal gradients

The effect of cross diffusion namely Soret coefficient and Dufour coefficient on the double diffusive convection in an unbounded vertically stratified two component system with compensating horizontal thermal and solute gradients is investigated in this paper. The conditions for the onset of stationary instability and oscillatory instability are established by the use of normal mode analysis. The effect of various physical parameters on the stability of the system is shown graphically. It is shown that the maximum growth rate of instability, the slope of the wave front and the wave number depend on both Soret and Dufour parameters. We also found the flux ratio corresponding to the maximum growth rate. Some of the known results of the former problems are deduced as special cases.     

A Method to Increase the Lateral Reversible Region of Bulk YBCO Above a Permanent Magnet Guideway

Lateral reversible region of the bulk high-T _c superconductor (HTSC) above the permanent magnet guideway (PMG) is a key parameter for the high-T _c superconducting (HTS) maglev system. The lateral stability and guidance force are proportional to the width of the lateral reversible region. When the lateral displacement of the bulk HTSC exceeds the reversible region, the maglev system will return to a new lateral equilibrium position. The method with the use of pre-displacement can successfully increases the lateral reversible region of the bulk HTSC. By the correct choice of the maximum lateral offset and a new starting point, the instability of flux motion can be suppressed. Unsuitable usage of this method will cause the intersection of guidance force and reduce the reversible region. Analyses based on the magnetizing history and pinning metamorphoses well explain the experimental results. Difference between this method and the pre-load method is also discussed in this article.     

Hydrodynamic stability of chemical equilibrium

In this article, which is partially expository, an elementary argument showing that chemical equilibrium for a model, reversible reaction is neutrally stable to small perturbations is presented. A standard hydrodynamic stability proof is given and the eigenvalues are computed using elementary asymptotics.     

具有脉冲效应的Holling—Tanner捕食-被捕食系统的正周期解

为了描述突然性因素对捕食一被捕食系统的影响,本文建立了具有固定时刻脉冲影响的Holling-Tanner捕食-被捕食系统模型,研究了系统的正周期解的存在性.利用基于叠合度理论的连续定理,证明了模型的正T-周期解的存在性,给出了系统存在正周期解的条件,该条件由两个种群的内禀增长率、脉冲周期及一个脉冲周期内的脉冲影响总量给出,这说明脉冲影响可能导致种群系统的平衡状态发生改变.     

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.     

Scanning electrochemical microscopy. 57. SECM tip voltammetry at different substrate potentials under quasi-steady-state and steady-state conditions

We discuss SECM tip voltammetry, where a UME tip is held above a conductive substrate within about a tip radius and a tip voltammogram is recorded as its potential is slowly scanned while the substrate is held at a fixed potential. When the potential of the substrate is changed, the series of steady-state tip voltammograms provide information about the reactants and products. When the potential of the substrate, ES, is set so that the reaction at the substrate is opposite to that at the tip (the usual SECM conditions), a total positive feedback (tpf) tip voltammogram is recorded. When the substrate potential is set to values where the reaction at the substrate is the same as that occurring on the tip, the tip is shielded from the species in the bulk solution. Depending upon the substrate potential, this can cause total shielding (ts) or a voltammogram that is the result of partial feedback/partial shielding (pf-ps). The result is a series of tip voltammograms that are characterized by tpf, pf-ps, or ts, depending upon ES. Experimental tip voltammograms resulting from the reversible reduction of TCNQ and oxidation of ferrocene in MeCN are reported. These are compared with those from simulations and approximate equations developed to describe the features of the tip voltammograms generated under tpf, ts, or pf-ps conditions. The effect of the diffusion coefficient ratio on the ability of the UME tip to reach a true steady state is also addressed and possible applications, e.g., obtaining information about the reversibility of an electrochemical reaction, the product of an electrochemical reaction, the stability of that product, or the diffusion coefficients of the electroactive species, are discussed.     

氮化钼膜电极制备工艺及其电化学行为的研究

研究了氮化钼膜电极的浸渍－煅烧法制备工艺条件及其电化学行为．试验结果表明,浸渍－煅烧法制备高活性氮化钼电极适宜的浸渍干燥温度为５１３～４７３Ｋ,煅烧升温速率为１Ｋ·ｍｉｎ^－１,煅烧温度为９９０Ｋ,煅烧时间为２ｈ;冷却方式为在氨气保护下随炉降温;浸渍－煅烧法制备的氮化钼电极成膜均匀,与基体附着性强;在－０．２２～０．３６Ｖ（ｖｓ ＳＣＥ）电位范围内,循环伏安图基本上呈现矩形,当扫描速度ｓ≤１００ｍＶ·ｓ^－１时,电流密度与电势扫描速度成正比,电极电容特征显著,动力学可逆性好,稳定性与重现性好．     

预防接种情况下非线性饱和接触率SIR流行病模型动力学性态研究

研究了一类预防接种情况下具有一般非线性饱和接触率SIR流行病模型动力学性态。得到决定疾病灭绝和持续生存的基本再生数。当基本再生数小于等于1时，仅存在无病平衡态：当基本再生数大于1时，除存在无病平衡态外，还存在惟一的地方病平衡态。利用Hurwitz判据、Liapunov-Lasalle不变集原理得到各个平衡态局部渐近稳定及无病平衡态全局渐近稳定的条件。特别地。当传染率为双线性时，无病平衡态及地方病平衡态全局渐近稳定。