带有时滞的非定常企业投资系统的Lyapunov稳定性

讨论了企业投资系统的Lyapunov稳定性,得到了企业投资系统渐进稳定的充分条件和稳定的必要条件,并给出了企业投资系统的临界积累率的表达式,这个问题的研究对于促进我国经济高速、稳定持续增长具有重要的理论意义和现实指导价值.     

时滞正系统全时滞稳定性的简单代数判别及其性质

在社会经济系统中,广泛地存在着多重时滞的正系统.对于连续型时滞正系统的全时滞稳定问题,文献[1]已给出简单而实用的代数判别方法.本文通过对离散型多重时滞正系统的深入研究,给出一个全时滞稳定的简单代数充要判别方法,并建立了时滞系统渐近稳定与时滞系统全时滞稳定之间的等价关系,避免了在稳定性判别中由于大量状态扩展所带来的困难.此外本文还建立了稳定性与正平衡点之间的等价关系,并讨论了系数     

一类带有比例相关捕获函数的时滞微分代数经济系统的Hopf分支分析

本文研究了一类用更为合理的无选择性捕获函数来代替普通的单位捕捞鱼获量函数的微分代数经济系统. 利用范式定理和中心流形定理, 获得了生物经济系统内平衡点局部稳定和Hopf分支的稳定性,改进和推广了已有的结果. 最后, 用数值模拟来证明分析结果的有效性.     

广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是一个非常重要的问题 ,由于广义大系统的复杂性 ,对其稳定性的研究也是一件相当困难的事情 .本文利用 Lyapunov方程 ,应用 Lyapunov函数法 ,研究了广义线性大系统和广义非线性大系统的稳定性和不稳定性 ,得到了系统的关联稳定参数域和不稳定域 .给出例子说明该方法的可行性 .     

一类带有比例相关捕获函数的时滞微分代数经济系统的Hopf分支分析（英文）

本文研究了一类用更为合理的无选择性捕获函数来代替普通的单位捕捞鱼获量函数的微分代数经济系统.利用范式定理和中心流形定理,获得了生物经济系统内平衡点局部稳定和Hopf分支的稳定性,改进和推广了已有的结果.最后,用数值模拟来证明分析结果的有效性.     

一类离散捕食系统在半开放资源下的捕获策略

对一类具有捕获的离散捕食系统,给出了正平衡点存在性和稳定性的条件.在半开放资源下考虑了可变价格及可变成本对捕获的影响,利用Gordon理论及政府征税政策,得到了经济均衡点的稳定条件,给出最优捕获策略.     

一类非线性的经济系统控制模型的稳定性分析

用边界比较法讨论了以CE S生产函数作为反馈的定常经济系统控制模型的稳定性,该模型为含有非局部条件的分布参数系统.并且证明了非定常模型的平衡解是全局渐进稳定的.     

初始时刻不同的奇异系统的稳定性

给出了初始时刻不同的奇异系统实用稳定性的定义,利用比较原理和Lyapunov函数方法研究了初始时刻不同的奇异系统的实用稳定问题,并得到了系统实用稳定性的判定准则.     

双参数对广义Hamilton系统稳定性的影响

研究双参数对带附加项的广义Hamilton系统稳定性的影响.首先将该系统在一定条件下化成梯度系统.其次利用梯度系统的特性来研究这类系统的稳定性及其对双参数的依赖关系.再次在参数平面给出稳定性区域.结果表明,该系统的平衡稳定性随双参数变化可能是稳定的,或渐近稳定的,也可能是不稳定的,相应给出各种稳定性对应的参数变化范围.     

具有扩散影响的Hopfield型神经网络的全局渐近稳定性

对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究.在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件.通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性.所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性.     

Asymptotic stability of neutral differential systems with many delays

We are concerned with delay-independent asymptotic stability of linear system of neutral differential equations. We first establish a sufficient and necessary condition for the system to be delay-independently asymptotically stable, and then give some equivalent stability conditions. This paper improves many recent results on the asymptotic stability in the literature. One example is given to show that the sufficient and necessary condition is easy to verify.     

The stability of non-conservative systems and an estimate of the domain of attraction

The stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces act, is investigated. The condition for asymptotic stability is obtained using the Lyapunov function and an estimate of the domain of attraction is also found in terms of the system being considered. A precessional system is also examined. It is shown that the condition for the asymptotic stability of a system is the condition of acceptability in the sense of the stability of a precessional system. The results obtained are applied to the problem of the stabilization, using external moments, of the steady motion of a balanced gyroscope in gimbals.     

四阶非线性系统的全局渐近稳定性

运用构造李雅普诺夫函数的方法 ,研究了一类四阶非线性系统的全局渐近稳定性 ,给出了该系统零解全局渐近稳定的充分条件     

Limiting Transition in a Singularly Perturbed System of Functional-Differential Equations

This article examines the asymptotic behavior of solutions of a singularly perturbed system of functional-differential equations of the retarded type with a small retardation. Sufficient conditions are introduced to guarantee convergence of the solutions of the system to the corresponding solutions of the limiting system for the case in which the basic condition of the classical Tikhonov theorem on the limiting transition in a singularly perturbed system, i.e., the condition of uniform asymptotic stability of the stationary point of the adjunct system, is replaced by a weaker Lyapunov condition for nonasymptotic stability. Dropping the Tikhonov condition is shown to expand the boundary layer within which the uniformity of the limiting solution breaks down.     

On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping

We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinite-dimensional then the system needs not being asymptotically stable (not even in the weak sense). Exponential stability is recovered under a generalized observability inequality, allowing for time-domains that are not intervals. Weak asymptotic stability is obtained under a similarly generalized unique continuation principle. Finally, strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition, evaluating their total contribution to the decay of the trajectories of the damped system. Our results are discussed using the example of the wave equation, Schrödinger?s equation and, for strong stability, also the special case of finite-dimensional systems.     

Dynamics of the density dependent predator-prey system with Beddington-DeAngelis functional response

Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.     

二阶非线性微分方程零解的全局渐近稳定性

对于二阶非线性微分方程零解的全局渐近稳定性的研究,含一,二个非线性项的研究成果较多,非线性项在两个以上的研究成果较少,本文研究具有四个非线性项的问题,而具去掉了一般要求Liapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界。     

Stability, Convergence, and Conditioning of Stationary Iterative Methods of the Form x(I+1)=Px(I)+q for the Solution of Linear Systems

A statistical approach to the study of the stability of a stationaryiterative method for solving a linear system x=Px+q is studied.An asymptotic stability factor is introduced. The relationsbetween this stability measure, the spectral radius of the iterationmatrix, and the condition number of the system are studied.The special case when the iteration matrix is normal is treatedseparately from the general one. For iteration matrices thatare normal, the following logical implications are found: large condition number large asymptotic stability factor poorconvergence. In the general case, a large asymptotic stability factor doesnot imply poor convergence, i.e.: large condition number large asymptotic stability factor poorconvergence.     

A global asymptotic stability condition for a Lotka–Volterra model with indirect interactions

A two-species Lotka–Volterra model extended with an arbitrary number of indirect interactions through diffusible and renewable compounds is presented in view of its considerable interest to the microbial community modelling. After the determination of the system’s fixed points and a short discussion over their local asymptotic stability, Lyapunov’s second method is applied to derive a sufficient condition of global asymptotic stability. Biologically, this condition indicates the necessity for one microbial type to show strong self-inhibition and the compounds to be quickly replaced.