具有时滞的食饵-捕食者模型的分支问题

研究一类具有时滞和比率依赖型功能反应函数的食饵-捕食者模型的动力学行为,分析表明系统的渐近稳定关键依赖于时滞.通过选择时滞作为参数,分析了系统从正平衡点处产生极限环的Hopf分支问题,同时得到了系统正平衡点稳定的时滞范围为0＜τ＜τ+,给出数值模拟验证了作者所得结果的正确性.最后给出本文的主要结论:当τ∈[0,τ0)时,系统(2)的平衡点是渐近稳定的,当τ=τjk,k=1,2,3,4;j=0,1,2,…时,系统(2)在平衡点附近产生Hopf分支,时滞长度为τ+.     

一类具有时滞和脉冲接种的SEIRS传染病模型

研究了一类具有时滞和脉冲接种的SEIRS传染病模型,应用脉冲微分方程比较定理和分析的方法得到了无病周期解的全局吸引性和系统持久性的充分条件,结果表明了时滞、非线性发生率、脉冲接种以及免疫力丧失对模型动力学性质的影响.     

一类具时滞的Gompertz捕食模型的稳定性分析

研究一类具有时滞的Gompertz增长率的捕食-被捕食模型,通过分析特征方程讨论了正平衡点的局部稳定性;通过构造适当的Lyapunov泛函,得到了保证系统正平衡点全局渐近稳定的充分条件,并讨论了在正平衡点附近Hopf分支的存在性问题.当τ=0时,应用微分方程定性理论,得到了系统存在极限环的充分条件.     

一类具有时滞的SIRS传染病模型的研究

研究了一类具有时滞的SIRS传染病模型,利用对模型的分析,得到了疾病灭绝与否的基本再生数,给出了无病平衡点的全局吸引性及地方病平衡点稳定性的存在条件,证明了疾病的持久性.     

一类生态-流行病模型正平衡解的存在性

考虑一类捕食者带有传染病并具有Holling-Ⅱ功能性反应函数的生态-流行病模型.讨论其带有扩散项的在齐次Neumann边界条件下问题.主要考虑其对应的平衡态问题的正解的存在性.首先应用最大值原理和Harnack不等式给出其反应扩散问题的正平衡解的先验估计(正的上下界估计),然后应用能量方法给出了该问题非常数正平衡解的不存在性,最后应用拓扑度理论研究了该问题非常数正平衡解的存在性.     

一类具有人口流动的SIR传染病模型

建立了一类带有人口流动的SIR传染病模型,运用特征方程及辅助系统证明了无病平衡点的全局稳定性,得到了疾病在斑块间持续的条件.     

具有扩散现象的非自治四维生态流行病模型的稳定性分析

建立并分析了具有扩散现象的非自治四维生态流行病模型,得到了系统持久生存的充分条件;基于Brouwer不动点定理,证明了系统周期解的存在性,同时通过构造Lyapunov泛函得到该系统周期解的唯一性与全局渐近稳定性,并给出了合理的生态解释.最后,通过一个数值例子说明了结论的有效性.     

一类不确定时滞大系统的分散模型参考自适应控制

运用分散模型参考自适应控制方法研究了一类不确定时滞大系统问题.在选择参考模型时,根据系统所期望的性能指标,考虑各子系统的相互作用,保留了互联项.这类不确定大系统的关联及干扰是时变不确定的.在这种不确定性界存在但却未知的情形下,基于Lyapunov稳定性理论,给出了其分散自适应控制律,并证明了整个互联大系统是一致最终有界的.     

一类非线性自治大系统的全局稳定性

本文研究非线性自治大系统
$\\frac{{{\\rm{d}}{{\\rm{x}}_{\\rm{i}}}}}{{{\\rm{dt}}}}=\\sum\\limits_{{\\rm{i}}=1}^{\\rm{r}} {{{\\rm{f}}_{{\\rm{ij}}}}({\\rm{xj}})({\\rm{i}}=1,\\ldots,{\\rm{r}})} $
这里,x_i∈Rⁿⁱ,f_ij∈C(R^nj,Rⁿⁱ,f_ij(o)=0,得到保证其零解为全局一致渐近稳定的充分条件(见定理1)。     

一类生产过程模型稳定性的决策分析

应用系统优化方法对一类生产过程建立系统模型,在稳定性分析的基础上应用控制论中极点配置理论方法对系统作决策分析.结果表明,优化策略下系统达稳时间短,生产利用率高.     

基于变权联系云的采空区稳定性二维评价模型

针对采空区稳定性评价具有模糊性、随机性以及评价指标等级呈有限区间正态分布等问题,考虑评价指标值突变对评价指标权重的影响,提出了基于变权联系云的采空区稳定性二维评价模型。首先选取12个评价指标构建采空区评价指标体系,并通过各指标联系云图反映其实际分布情况;然后利用博弈论和变权理论得到变权权重;最后计算采空区各评价指标对应等级的确定度和采空区的综合确定度,并根据最大隶属度原则确定采空区稳定性等级。为解决指标等级归属不一致的问题,引入模糊熵作为第二维评价系统,以表征采空区稳定性的复杂度。结果表明:变权联系云模型评价结果与实例应用结果一致,验证了该模型的可行性与合理性。     

The Representation of Four Personality Disorders by the Schedule for Nonadaptive and Adaptive Personality Dimensional Model of Personality.

This study examined the relationships of the Schedule for Nonadaptive and Adaptive Personality (SNAP) model of personality to 4 targeted personality disorders (PDs) in a large multisite sample of patients. Data were examined from 529 patients, who were assigned 1 of 5 primary diagnoses: borderline, schizotypal, avoidant, and obsessive-compulsive PDs and major depression without PD. Patients were administered the SNAP questionnaire and results were compared among diagnostic groups and between patient groups and nonclinical norms. Results indicated that the dimensions of the model appear to have considerable promise in differentiating normal from abnormal personality, particularly in the propensity of individuals with PDs to manifest negative affects and interpersonal detachment. Furthermore, the model appeared to successfully distinguish specific PDs, a property that represents a particular challenge for dimensional models of personality. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一类具反馈控制的病毒感染模型的稳定性与周期解

研究了一类具有反馈控制的病毒感染动力学模型.利用常微分方程定性与稳定性方法,通过分析特征方程,讨论了该模型各个平衡点的局部稳定性;通过构造适当的Lyapunov泛函,证明了未感染平衡点和反馈控制病毒感染平衡点的全局稳定性;最后,利用重合度理论中的延拓定理,给出了保证其周期系统存在正周期解的充分条件.     

四辊轧机工作辊辊系稳定性探讨

主要从附加弯矩、摩擦弯矩和附加水平力等方面对四辊轧机工作辊辊系的稳定性进行了全面地分析 ,并建立了影响辊系稳定性的力学模型 ,为确定辊系最佳偏移距提供了理论依据。     

Modeling and Measurements of Intermixing Time in a Water Model of a Four Strand Steelmaking Tundish System

Intermixing of two different grades of steel in a 17 tonne, 4 strand bloom casting has been investigated in a ~0.3 scale, geometrically and dynamically similar, isothermal water model tundish system. In this, intermixing phenomena were studied by simulating mixing of flowing water in the tundish, having different dissolved tracer (electrolyte) concentrations. Electrical conductivity measurement technique was employed to monitor concentration of dissolved electrolyte near the strands as a function of time and thereby determine intermixing time. For each experimental condition, three measurements were made and based on such an average intermixing time was estimated. Reproducibility was found to be always within ±15 %. Influence of key operating variables such as, inflow rate from ladle, net outflow rate from tundish, residual liquid volume left over from the previous grade etc. on the duration over which intermixing occurs (referred to as in the text as the intermixing time) was investigated. It was found that any increase in residual volume as well as inflow rate tends to prolong intermixing time. In contrast, influence of outflow rate was quite the opposite. Furthermore, while variation of intermixing time among strands was only marginal, tundish interior design (viz., presence of flow modifiers, pouring box etc.) was found to have considerable influence on intermixing time. Flow phenomena (observed visually through the dispersion of KMnO₄ solution) in the given tundish was found to be practically symmetrical about the transverse centre-line and so was the associated intermixing time. Embodying a large number of experimental data, explicit correlations for intermixing time were derived in terms of principal operating variables through dimensional analysis and regression. Two different versions of correlations, applicable respectively to a flat bottom as well as a wedge fitted tundish systems, were developed. In SI unit, these are respectively represented as:

1. $ {{\uptau}}_{{{\text{int}}.{\text{mix}}}} = 6.38 \times V_{\text{res}}^{0.86} Q_{\text{in}}^{0.48} Q_{{{\text{out}},{\text{T}}}}^{ - 1.32} $ τ int . mix = 6.38 × V res 0.86 Q in 0.48 Q out , T ? 1.32
2. $ {{\uptau}}_{{{\text{int}}.{\text{mix}}}} = 1.43 \times 10^{ - 2} V_{\text{res}}^{1.7} Q_{\text{in}}^{ - 0.02} Q_{{{\text{out}},{\text{T}}}}^{ - 1.82} $ τ int . mix = 1.43 × 10 ? 2 V res 1.7 Q in ? 0.02 Q out , T ? 1.82

in which, Q _in is the input flow rate, Q _out,T is the net outflow rate, V _res is the residual liquid volume and τ _int.mix is the intermixing time corresponding to a degree of 95 % homogeneity. Finally, adequacy and appropriateness of the proposed correlations are assessed both from theoretical and experimental stand points.     

增量型AGC模型稳定性研究

采用误差分析方法导出增量型自动厚度控制(AGC)模型设定序列的差分方程.根据该差分方程的特征值表达式讨论了AGC模型设定序列的稳定区域和稳态误差与AGC模型参数之间的关系.     

轧机微尺度行为和四列圆锥轴承寿命

2辊或4辊轧机的辊系，对工作辊四列圆锥轴承满寿可靠运行起至关重要甚至决定性作用。在轧制力或弯辊力下的轧辊弹性弯曲变形微尺度行为，破坏辊系的静定条件，致使四列圆锥轴承异常偏载；机架窗口内有隙轴承座在外干扰力矩作用下，引起轧辊的动态交叉微尺度行为产生异常轴向力，使四列圆锥轴承超载。对此，为定量描述圆锥轴承三维载荷分布特性，给出大型轧机四列圆锥滚子轴承三维载荷数值解法，以轴承的滚子载荷工况评估多列圆锥轴承的实际寿命，取代现有机械设计和轧机设计理论中的总体轴承工况寿命评估法。