具时滞的人类呼吸系统模型的稳定性与分支

研究了描述人类呼吸系统的具时滞的二维微分方程的平凡解的稳定性和Hopf分支．利用规范型理论和中心流形定理给出了关于分支周期解的稳定性及Hopf分支方向等的计算公式,且进行了数值模拟计算．     

具时滞的二维神经网络模型的分支

研究了一类具时滞的二维神经网络模型．通过对该模型的特征方程根的分布分析, 在适当的参数平面上给出了分支图．得到了pitchfork分支曲线是一条直线,进而研究了每个平衡点的稳定性和Hopf分支的存在性．最后,利用规范性方法和中心流形理论,得到了Hopf分支的分支方向和分支周期界的稳定性．     

以滞量为参数的广义Liénard方程的Hopf分支

本文讨论广义Lienard方程的Hopf分支问题首先指出文［3］的错误，并分析了时滞对周期的影响，估计出k＝－f（O）可取多少个不同的值使广义Lienard方程有周期解．然后考虑以时滞r为参数的Hopf分支问题，得到了Hopf分支值及分支方向，并估计出时滞r可取多少个不同的值使方程有周期解，再运用Hassard“规范形”方法，给出了计算以滞量为参数的Lienard方程的Hopf分支公式，利用该公式，能判断周期解的稳定性井得到周期解的近似表达式．     

一类具有混沌同步的Lorenz时滞系统的稳定性分析

研究一类具有混沌同步的Lorenz时滞系统在零平衡点处的稳定性以及Hopf分支,得到了系统的稳定性稳定性开关和Hopf分支出现的条件,并讨论出分支周期解的分支方向、稳定性和分支周期的变化律.最后,做了一些数值以验证理论分析的正确性,并模拟出正平衡点产生稳定的周期解.     

一类时滞自催化反应扩散方程的周期解

研究化学中一类时滞自催化反应扩散方程在Neumann边值条件下的稳定性和Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用中心流形和规范型理论讨论其分支周期解的分支方向和稳定性及分支周期的交化律.     

具时滞能源价格模型的动力学性质

以滞量τ为分支参数,研究了具时滞的能源价格模型的动力学行为,这些行为包括:系统在平衡点附近的稳定性,局部Hopf分支的存在性,发生条件.Hopf分支的方向,分支周期解的稳定性以及分支随参数变化其周期解的周期变化.最后通过数值模拟验证了理论分析结果,并用分支理论解释了能源价格模型产生且维持周期振荡的原因.     

参数依赖时滞的Nicholson生态模型的稳定性和分支

研究了参数依赖时滞的Nicholson生态模型的稳定性和分支问题.利用几何分析方法和摄动法,给出了系统唯一正平衡态的稳定性和Hopf分支存在条件,得到了分支周期解的近似解析表达式和周期解稳定性判别式,通过若干实例验证了理论分析和数值计算的一致性.     

一类微气泡耦合时滞系统的周期解

研究一类微气泡耦合时滞系统的稳定性以及Hopf分支,得到了稳定性和Hopf分支出现的条件,并利用泛函微分方程相关理论讨论出分支周期解的分支方向、稳定性和分支周期的变化律.     

温盐双扩散系统对流扩散周期解的线性与非线性稳定性分析

本文对温盐双扩散系统的稳定性问题引入了一种简洁的强非线性自治系统稳定性的分析方法，用摄动理论得到了无穷小运动下线性周期解的单调与振荡分支的存在范围及有限振幅运动下非线性周期解的振荡分支在０＜ｒｓ－ｒｓｃ＜＜１条件下的存在区域及稳定性区域，给出了不同涡旋方向下的稳定性结论．     

一类带有扩散和时滞的捕食与被捕食模型的渐近性质

本文中，我们考虑一类带有扩散和时滞的捕食与被捕食系统．我们分析了系统的非负不变性，边界平衡点性质，全局渐近稳定性及永久持续生存性．在这一系统中，当时滞由0变到ro时，系统在平衡点附近发生Hopf分支．即当r增加通过临界值ro时，从正平衡点分支出周期解．     

The stability and stabilization of the motion of non-conservative mechanical systems

Two stability problems are solved. In the first, the stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces (systems of general form) act, is investigated. The stability is considered in the case when the potential energy has a maximum at equilibrium. The condition for asymptotic stability is obtained by constructing Lyapunov's function. In the second problem, the possibility of stabilizing a gyroscopic system with two degrees of freedom up to asymptotic stability using non-linear dissipative and positional non-conservative forces is investigated. Stability of the gyroscopic system is achieved by gyroscopic stabilization. The stability conditions are obtained in terms of the system parameters. Cases when the gyroscopic stabilization is disrupted by these non-linear forces are indicated.     

Stability analysis of data-driven local model networks

This article discusses stability analysis of data-driven dynamic local model networks. In contrast to traditional fuzzy modelling, the structure and complexity of such model architectures is not unique when only observed input- and output data are available for their parametrization. The present article complements the well-known trade-off between accuracy and complexity by the notion of stability. For this purpose, existing Lyapunov stability criteria for local model networks are extended by a decay rate which represents a scalar and quantitative stability measure. It allows to compare models with different degrees of complexity also in view of their stability. For some of the commonly available Lyapunov stability criteria, the individual local model transitions are crucial. Therefore, in this article, an approach is introduced to determine the actually occurring model transitions by means of the identification data. The methods presented in the article are illustrated and discussed by means of a simulation example. It is shown how model complexity and the related approximation quality can have an adverse impact on the stability and how the outcome of different Lyapunov criteria is affected by the proper determination of local model transitions.     

On the stability of inhomogeneously viscoelastic reinforced bars

There is investigated the stability of inhomogeneously ageing reinforced viscoelastic bars. It is assumed that the strains and stresses in the reinforcement are related by Hooke's law. The properties of the matrix material are described by equations of the theory of viscoelasticity of inhomogeneously ageing solids /1,2/. Under different boundary conditions for the ends of the bar and loading methods an expression is set up for the critical force in stability problems in an infinite time interval. The stability definition taken corresponds to the Liapunov stability definition for the motion of dynamical systems. Estimates of the critical time when the magnitude of the deflection of a viscoelastic bar reaches a given value are obtained for stability problems in a finite time interval. The formulation for the stability problem in a finite time interval starts from the definition of stability of motion of dynamical systems by taking its beginning from the Chetaev work. The dependence of the critical time on the inhomogeneity and the reinforcing parameter is investigated numerically. The stability of viscoelastic unreinforced bars was studied in /3,4/, A survey and bibliography of research associated with the stability problem for viscoelastic bars are available in /5–8/.     

The effect of density-dependent dispersal on the stability of populations

The nonlinear stability of two populations diffusing in a common bounded domain with nonlinear density-dependent dispersal of a general type is studied, under Robin boundary conditions. The stability and instability of the positive equilibrium are studied by the linear eigenvalues method. The nonlinear stability is studied with the Lyapunov direct method. In a particular case, global stability has been obtained.     

首次积分与临界情形运动稳定性

本文指出1946年苏联学者Четаев提出用首次积分的线性组合来构造李雅普诺夫函数后Четаев及其学生们解决保守系统的运动稳定性问题均用此方法.但是由于用试凑的方法解决起来比较麻烦,而且用他们的方法所得出的稳定性条件也不够完全,只能解决问题的纯虚根的情形,零根的情形却未考虑.本文提出利用降阶方法,也就是将微分方程通过消除循环坐标变换成标准形式,这样稳定性条件可直接由能量积分得出,用此方法计算起来不仅很简捷,而且零根情形亦可以考虑.因此对于具有两个循环坐标问题可以化成二阶系统并且很简捷地得到稳定性条件新结论.至于一个循环坐标问题,事实上Четаев及其学生们并未解决,例如外环为水平或任意角的陀螺仪的运动稳定性问题,但是用我们的方法却给出条件稳定与不稳定的条件.     

时变离散大系统的稳定性

本文首先给出了线性时变离散系统稳定性的一个充分条件.然后研究当孤立子系统满足上述条件时的线性及非线性时变离散大系统的稳定性.利用向量李雅普诺夫函数法结合时变离散系统的比较原理,得到了时变离散大系统在稳定性中的集结模型.直接由集结系统的稳定性得到大系统稳定性的条件.     

Stability of reaction-fronts in porous media

The stability of reaction-fronts in porous media is studied with analytical and numerical methods. A stability criterion has been derived using linear stability analysis assuming a sharp font. The sharp front assumption is an approximation of the mathematical model in the limit of an infinite rapid reaction. The criterion shows that the stability of a sharp reaction front is dependent on the permeability that develops behind it. The sharp front is unstable for perturbations of any wave-length if the permeability increases behind the front. The criterion shows that short wave-length perturbations are more unstable than long wave-length perturbations. The sharp front is labile when the permeabilities are the same at both sides of the front. This means that the perturbed front moves unchanged forward. Finally, perturbations will die out in case the permeability decreases behind the sharp front. The stability of non-sharp fronts are simulated numerically when dissolution is by first order kinetics, the transport is by convection and diffusion and when the permeability and specific reactive surface depends on the porosity. The numerical experiments behave according to the stability criterion.     

假设检验的相对稳定性

郑祖康^[1]提出了数理统计学中一个有意义的新问题－假设检验的稳定性。但是,由于稳定性定义的条件太强,从而通常检验统计量的稳定性并不好。本文根据假设检验的实际意义,定义了假设检验的相对稳定性,讨论了一类常用检验统计量的相对稳定性的一些性质,作为特例,得到似然比检验的相对稳定性的性质。     

Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control

This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative (PID for short) boundary control is addressed. In the proportional-integral (PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system subject to PID control is always unstable.     

Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.