线性时滞系统实用稳定性的一个简明判据

利用比较的方法，获得了线性时滞系统实用稳定性的一个简单判定定理．     

Numerical Determination of the Instability Region for a Delay Model of Phage–Bacteria Interaction

In this paper we describe an algorithm to determine the instability region of the endemic equilibrium of a delay model for phage–bacteria interaction in open marine environment. The algorithm relies on a new geometric criterion for stability switches introduced by Beretta and Kuang for delay models for which the corresponding characteristic equations have delay-dependent coefficients [6]. The outputs of the algorithm presented in this paper, which can be equivalently applied to similar 2D delay models, show that for this kind of models large delays are usually stabilizing.     

具有限时滞一阶线性泛函微分方程的稳定性区域划分

讨论了一阶线性有限时滞泛函微分方程的稳定性区域,用一个超平面把参数空间划分为不同的稳定性区域.这个超平面上的每一点对应于特征方程在纯虚轴上至少存在一个零根(原点除外),所得结论可用于Hofp分枝分析和控制理论.     

Stability of implicit-explicit linear multistep methods for ordinary and delay differential equations

Stability properties of implicit-explicit (IMEX) linear multistep methods for ordinary and delay differential equations are analyzed on the basis of stability regions defined by using scalar test equations. The analysis is closely related to the stability analysis of the standard linear multistep methods for delay differential equations. A new second-order IMEX method which has approximately the same stability region as that of the IMEX Euler method, the simplest IMEX method of order 1, is proposed. Some numerical results are also presented which show superiority of the new method.      

二次滞后离散奇异系统的吸引域

本文利用Lyapunov方法对二次滞后离散奇异系统进行定性、定量分析并给出了该类系统的零解一致稳定吸引域和渐近稳定吸引域的定量估计.当初始扰动是在渐近稳定吸引域时,二次时滞离散广义系统的初始值问题的解趋于零.发现这些判据与滞后无关,容易测试,便于工程上的应用.通过示例描述了该方法的应用.     

Delay-dependent and delay-independent stability criteria for a delay differential system

For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.

     

时滞微分方程定常解稳定性改变的几何判别法

针对一类系数含时滞的时滞微分方程,讨论了时滞对微分方程定常解稳定性的影响,建立了定常解稳定性发生改变的几何判别法.     

Stability in linear multistep methods for pure delay equations

The stability regions of linear multistep methods for pure delay equations are compared with the stability region of the delay equation itself. A criterion is derived stating when the numerical stability region contains the analytical stability region. This criterion yields an upper bound for the integration step (conditional Q-stability). These bounds are computed for the Adams-Bashforth, Adams-Moulton and backward differentiation methods of orders ?8. Furthermore, symmetric Adams methods are considered which are shown to be unconditionally Q-stable. Finally, the extended backward differentiation methods of Cash are analysed.     

THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS

1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f…