查询词典 asymptotic stability

Algorithm application of neural networks.Ⅲ Implementation of neuro-computers. The main contribution of the dissertation can be summarized as follows: 1 Hopf bifurcation of three kind of neural networks are discussed in detail, including type of discrete time delay, type of time delay with weak kernel and strong kernel as well as the proof of existence of bifurcation. Other problems such as asymptotic stability of bifurcation periodic solution, algorithm of determining the bifurcation direction, asymptotic stability and style of periodic solution are also studied. The average time delay is chosen as the bifurcation parameter, phenomena pertinent to system states of the continuous time delay network with strong kernel evolving from stable to oscillating, then back to stable again are observed.

论文的主要创新之处可以归纳如下： 1）针对目前国内外对神经网络的分岔研究较少的情况，论文中详细讨论了带离散时延神经网络、带弱核的连续时延神经网络、带连续分布时延且具有强核的神经网络的Hopf分岔现象，从理论上证明了Hopf分岔的存在性，并研究了分岔周期解的渐近稳定性，得到了确定周期解的渐近稳定性、分岔方向、周期解的渐近形式的算法；用平均时延作为分岔参数，发现带强核的连续时延神经网络中存在着系统的状态由稳定变化到振荡现象，当继续增加平均时延参数时，又从振荡变为稳定这一特殊的动力学现象。

The conditions for the global asymptotic stability of the equilibrium point are expressed as the stability of the some decomposed matrix.

这种方法以矩阵分解为工具，结合平衡点的渐进稳定判据，用分解矩阵的稳定性决定平衡点的全局渐近稳定性。

We proposed and analyzed a class of Lesli predator-prey model with mutual interference and obtain global asymptotic stability of positive equilibrium point for the model by using the theory and method of stability.

建立并分析一类具有相互干扰的Leslit捕食与被捕食模型，运用稳定性理论及方法得到了该模型正平衡点的全局渐近稳定性。

Furthermore, based on the Lyapunov stability theorem, asymptotic stability results can be obtained.

此外，根据Lyapunov稳定理论，我们将能得到渐进稳定的结果。

The key idea is to reduce the global stability problem to the asymptotic stability of an uncertain discrete-time system.

主要思想是将所研究的极限环的全局稳定性问题转化为不确定离散系统的渐近稳定性问题。

We discussed the positive invariant set,the exsistence and the stability of the equilibrium by the stability theory of ordinary differential equation and the conditions for the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are obtained.

本文讨论了模型的正不变集，运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性，得出了疾病消除平衡点和地方病平衡点的全局渐进稳定的充分条件。

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

In chapter 2. to two classes of specific systems in engineering, we make researches into stability with respect to their own invariant sets through the theoretic techniques of HDS. And then we bring forward sufficient conditions of uniform asymptotic stability and exponential stability with respect to their own invariant sets in the sense of Lyapunov.

第二章针对实际工程之中的两类具体系统用混合动态系统的理论方法对其关于不变集的稳定性进行了研究，提出了它们关于各自的不变集在Lyapunov意义下一致渐近稳定、指数稳定的充分条件。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

A framework of stability theory including the definition of stability and asymptotic stability was put forward based on the model of DAHS.

建立了含有微分代数子系统的混杂系统的数学模型，并提出了包括该类混杂系统稳定性和渐近稳定性定义在内的理论框架。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。