稳定性条件

Paper studies the practical stability of electricity market models by tools, for example, the appropriate structure Lyapunov functions, Cauchy matrix, the matrix measure, constant variation. Judging practical stability sufficient conditions and estimating formula of ultimate convergence boundary are provided. Conditions are descriptive by coefficients of models. At the same time, paper studies the Lyapunov stability of the electricity market. As well as the sufficient conditions of judging electricity market Lyapunov stability are provided. Some of conclusions improved the results of Alvarado and others. The conclusion of Lyapunov stability has made a comparative with practical results.

首次将实用稳定性理论和方法应用于电力市场稳定性的研究中，借助于构造合适的Lyapunov函数、柯西矩阵、矩阵测度、常数变易法等工具，系统研究了所建电力市场模型的实用稳定性，得到了用模型的系数来描述其实用稳定性的一系列判定条件和最终收敛边界的估计公式；同时对电力市场的Lyapunov稳定性进行了研究，得到了电力市场稳定性的若干判据，部分结论改进了Alvarado等人的结果；随后将Lyapunov稳定的结果与实用稳定进行了比较。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utility function are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

Last we obtain globally asymptotically stability of boundary equilibrium by applying locally asymptotically stability and attractiveness and persistence by using uniform repeller theorem.

在第二章中研究了一类具有时滞的捕食与被捕食系统，分析了系统的正不变集，运用了特征值理论得到了边界平衡点性质，当时滞很小时，得到了系统在正平衡点局部渐近稳定的充分条件，以及当T增加到T_0时，系统在正平衡点附近产生Hopf分支的充分条件；利用局部渐近稳定性加吸引性得到了边界平衡点全局渐近稳定性的充分条件，且应用一致排斥定理得到了种群持久生存的条件。

Anisotropic Media ; Pseudospectral Method ; Elastic Wave Propagation ; Multi-Componet Records ; Stability Condition

各向异性介质；伪谱法；弹性波传播；多分量记录；稳定性条件

Formulas to determine the stability of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory.

三、分析了单源节点单连接节点的Kelly主算法，当稳定性条件被破坏后，系统表现出的动力学特性。

The convergence of this method is proved, and stability condition of the control system based on Lyapunov function is deduced.

首次证明了算法的收敛性，并基于Lyapunov方程推导了系统的稳定性条件。

The basic heat balance model,the temperature-salinity double diffusion model and the thermal stability model were discussed.

通过对上述模型的研究，文中探讨了太阳池内部稳定性条件和边界的变化规律。

In the design procedure, we do not need to know the specific values of the system parameters . We only require that the member functions of the input variable are triangular-shaped and the central values of the output variable member functions are selected in order to satisfy the stability expressions.

在模糊控制器的设计过程中，不需要知道对象的系统参数（A，b，c或A，B，C）的具体值，而只要求输入变量的隶属函数为三角形和输出变量的隶属函数中心值的取值满足稳定性条件所要求的关系式。

As to different types of network transmission delay and packet loss, it obtains the stability conditions for CNS.

针对网络传输时延、信息丢失等不同情况，分析和得到控制网络系统的稳定性条件。3。

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。