一类连续分布时滞模型的稳定性

本文应用 Ｌｙａｐｕｎｏｖ 泛函方法研究了一类具有连续分布的时滞模型　　 ｘ′ｉ（ｔ） ＝ － ｂｉｘｉ（ｔ） ＋ ∑ｎｊ＝ １ ωｉｊｆｊ ∫∞０ ｋｊ（ｓ）ｘｊ（ｔ－ ｓ）ｄｓ ＋ ｐｉ,　　（ｉ＝ １,２,…,ｎ）平衡点的全局渐近稳定性,获得了若干新的充分条件     

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。     

Stability Analysis of Grasps with a Robotic Multifingered Hand

Stability is a significant property for a robot hand grasp to perform complex tasks similar to human hands. The common method to investigate the stability of robotic multi-fingered grasp system is Lyapunov direct method, but usually it is rather difficult to construct a proper Lyapunov function.Avoiding the hard work of constructing a Lyapunov function , we propose the sufficient conditions for stability of the robotic grasp system.     

一类含两个非线性项的三阶拟线性微分方程解的稳定性

应用Lyapunov函数方法讨论一类含两个非线性项的三阶拟线性微分方程解的稳定性,得到了此类方程解的稳定性的若干新结果,同时推广了作者已有的结果。     

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。     

On the Stability of a Nonlinear Viscoelastic Rod Subjected to a Longitudinal Force in the Form of a Random Stationary Process

The stability and reliability of a nonlinear viscoelastic rod under a stochastic excitation is investigated. The loads are assumed to be in the form of random stationary processes. The solution is obtained with the help of a numerical method, which is based on the method of the statistical simulation of random input processes and on the numerical solution of the system of nonlinear and linearized integro-differential equations. These equations describe a nonperturbed and perturbed motion of the rod. The estimation of the stability is carried out with the help of top Lyapunov exponents.     

一类一般化的排队网络族的全稳定性

本文对一类有两个工作站的一般化的排队网络族给出了其全稳定的一个充分条件。     

具有吸毒年龄和治疗年龄的海洛因模型的全局稳定性（英）

本文建立了一个吸毒人群具有吸毒年龄,治疗人群具有治疗年龄的海洛因传播模型．得到了基本再生数．通过波动引理和李雅普诺夫泛函,证明了当基本再生数小于1时无海洛因吸食平衡点是全局渐近稳定的,当基本再生数大于1时,海洛因传播平衡点是全局渐近稳定的．     

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

本文对一类具有非线性发生率的SEIR传染病模型进行了研究.确定了决定疾病灭绝或持续存在的阈值-基本再生数,并分析了模型的平衡点的存在性;通过构造恰当的Lyapunov函数,运用La Salle不变性原理证明了当基本再生数小于或等于1时,无病平衡点是全局渐进稳定的;利用Lyapunov直接方法证明了当基本再生数大于1时,地方病平衡点是全局渐进稳定的.最后,将发生率具体化用数值模拟验证了所得理论分析结果的正确性.     

随机系统均方稳定性的Lyapunov型方程(英文)

研究随机系统的均方稳定性，得到了一个Ｌｙａｐｕｎｏｖ型方程，并证明随机系统是均方稳定的充分必要条件是该Ｌｙａｐｕｎｏｖ型方程有正定解。     

具有阶段结构和时滞比率依赖的捕食系统的持续生存和稳定性

本文研究了一类带有时滞和对捕食者进行分阶段的比率依赖的捕食模型,得到了该模型中的种群的持续生存的充分条件。通过构造Lyapunov泛函的方法,得到了该模型唯一正平衡点的局部稳定和全局稳定的充分条件。     

带时滞的传染病模型的全局稳定性

研究了一类SEIS传染病模型的全局稳定性，通过构造Liapunov泛函，证明了当潜伏期较小，染病期较长并且再生数接近于1时，该模型的地方病平衡点是全局渐近稳定的。     

Global asymptotic stability in a model of networks

Global asymptotic stability is of importance from a theoretical as well as an application point of view in several fields. We study a system of cubic polynomials that models biological networks. We classify the equilibria and show that the property that the interconnection matrix is Lyapunov diagonally stable is a key feature that determines convergence to a single equilibrium. The results are applied to chains of negative edges, cycles, and to interconnected graphs. We give numerical examples and study network graphs obtained from a model of the Drosophila circadian clock.     

一类分数阶非线性时滞系统的稳定性与镇定（英）

稳定性是控制系统分析与设计的基础．探索分数阶系统,特别是分数阶时滞非线性系统的稳定性条件是控制理论与工程领域中的难点问题．本文研究了一类分数阶非线性时滞系统的稳定性和镇定．通过将原系统转化成等价的分数阶积分系统,再借助不等式放缩技术,提出了一个有效且形式简单的确保该类系统稳定新的时滞无关稳定性准则．根据所得的稳定条件,提出了基于时滞线性反馈控制器的镇定控制方法．最后,数值实例验证了所得结果的有效性．此外,本文所使用的方法可以推广和应用于其他类型的分数阶系统的稳定性和镇定控制．     

一类变时滞非线性Lurie控制系统的绝对稳定性

应用Lyapunov函数方法讨论了一类变时滞非线性控制系统的绝对稳定性。得到Lurie控制系统绝对稳定的充分条件。文末用例了说明此方法的有效性。     

Superconductor Thermal Stability Under the Effect of a Two-Dimensional Dual-Phase-Lag Heat Conduction Model

The thermal stability of superconducting thick wire has been numerically investigated under the effect of a two-dimensional dual-phase-lag heat conduction model. Two types of superconductors are considered, Types I and II. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. Also, the superconductor thermal stability under the effect of different design, geometrical, and operating conditions is studied.     

一类具比例时滞细胞神经网络的全局渐近稳定性

本文应用M-矩阵理论和构造合适的Lyapunov泛函,对具比例时滞细胞神经网络进行研究,得到确保该系统的平衡点存在唯一与全局渐近稳定的时滞依赖的充分条件。其次通过变换将这个系统等价变换成具常时滞与变系数的细胞神经网络,再通过M-矩阵理论和构造合适的Lyapunov泛函,得到确保该网络平衡点存在唯一与全局渐近稳定的时滞独立的充分条件。最后给出两个数值算例验证所得结果的正确性和与以往结果相比较低的保守性,并根据比例时滞因子的情况,分析了所得时滞依赖与时滞独立的条件的适用范围。     

Experimental Investigations of Phase Equilibria in Binary Liquid Immiscible Alloys

Electroconductivity measurements for liquid metal (Tl, In)–chalcogen (Se, Te) alloys were performed in concentration range of their miscibility gaps. The experiments have been carried out under excess pressure of argon gas (up to 50 MPa) at temperatures up to 1200 K. Many-sectional measuring cell allows simultaneous determination of the electroconductivities of both separated liquids in entire range of the miscibility gap. The liquid–liquid coexistence curves for Tl–Se, Tl–Te, In–Se, and In–Te systems were constructed and critical point data were evaluated. The critical indices were also estimated. The results are analyzed in comparison to available data for fluid metals in vicinity of the liquid–vapor critical point.     

Model Calculation of Distance-Dependent Electron–Phonon Coupling Parameters Derived from One- and Two-Body Interactions for a Dimer

We evaluate all the electron–phonon coupling terms derived from one and two-body electronic interactions, in both the adiabatic and the extreme nonadiabatic limit, for a dimer with a nondegenerate orbital built from atomic wave functions of Gaussian shape. Different forms of the Hamiltonian contributions result in the two limits.     

一类带有成熟期的种群增长模型平衡点的稳定性

对一类带有成熟的种群增长模型进行研究，分析其正平衡点对应的特征方程，得到其局部稳定性随成熟期变化的完整结论。