Identification of certain noisy MA models: new results

In this paper, we address the identification problem of p-inputs q-outputs MA models, corrupted by a white noise with unknown covariance matrix, in the case where p<q. Under certain additional conditions, we show that the generating function of the MA model is identifiable (up to a p×p constant orthogonal matrix) from the autocovariance function of the observation. Our results extend those already obtained in Desbouvries et al. [5] and Desbouvries and Loubaton [6].     

一个三维种群模型的Hopf分枝

用分枝理论的方法研究三维种群模型的平衡点存在性、稳定性，证明了一个参数区域中，系统存在Ｈｏｐｆ型周期解，给出了确定Ｈｏｐｆ分枝值的方法，计算了Ｈｏｐｆ分枝的分枝方向及极限环稳定性的判定公式，揭示了自然界中食饵与捕食者相互依存现象的数学规律性。     

随机经济模型的Hopf分岔研究

运用非线性动力学理论对带有随机参数的微分方程经济模型的Hopf分岔进行了研究.首先,选择拱形分布的随机变量并利用Chebyshev正交多项式逼近法将经济模型转化为确定性等价系统.然后,运用Hopf分岔定理与Lyapunov系数相关理论研究了系统的稳定性和Hopf分岔的存在性等,结果显示随机参数对系统的稳定性具有很大影响.最后,运用数值仿真验证了系统具有平衡点渐近稳定性,并存在Hopf分岔现象.该研究结果可为调控和保持金融市场稳定提供理论参考.     

Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness

An asymptotic high-frequency solution is presented for the problem of diffraction of acoustic waves emanating from a ring source by a semi-infinite cylindrical pipe of certain wall thickness having different internal, external and end surface impedances. Through the application of the Fourier-transform technique in conjunction with the Mode Matching method, the diffraction problem is described by a modified Wiener–Hopf equation of the second kind and then solved approximately. Various numerical results illustrating the effects of the parameters of the problem on the diffraction phenomenon are presented.     

用动力系统理论研究多自由度非线性振动问题

运用中心流形定理和范式理论,本文推导出了一种计算n维动力系统Hopf分叉范式系数的简捷方法.这种方法还可用来求解多自由度非线性振动问题.用它求解比以往的各种近似方法简单、方便、易于掌握.现已将这种方法程序化,它可在IBM PC/XT,AT及其兼容机上使用.     

A model for numerical evaluation of the global stability region in power systems determined by a nonlinear limit cycle

A power system is a large dynamic system, which includes many nonlinear elements. According to the nonlinear analyses using Hopf bifurcation theory, it can be detected that a limit cycle exists around an operating point, which may affect the global stability of a power system significantly. The authors have presented a numerical method to analyze the nonlinear characteristics in power systems by observing the power swing after some perturbation where the coefficients of nonlinear terms are determined by the least squares method. In this paper the method is modified for the application to a longitudinally interconnected power system including an excitation system, and the influence of the excitation voltage limiter on the nonlinear phenomena of the whole power system can be detected by some numerical analyses. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(3): 17–27, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10193     

两个非线性系统Hopf分岔的状态反馈控制

本文简单介绍了Hopf分岔理论,对于Van der pol振子和一个发生亚临界Hopf分岔的二阶非线性系统分别设计了具有可变增益的状态反馈控制器,利用Lyapunov稳定性定理证明了在该控制器作用下,可以消除非线性系统的Hopf分岔现象,保证系统的渐近稳定,控制器与系统参数的变化范围无关,数值仿真也表明了这种控制方法的有效性.因此,对于发生Hopf分岔的非线性系统,可以通过设计合适的状态反馈控制器去消除 Hopf分岔,维持系统的渐近稳定,而不仅是延迟分岔的出现,扩大系统稳定运行的范围.     

一类具有阶段结构和饱和发生率的生态流行病模型的稳定性

本文研究一类食饵具有阶段结构且捕食者染病的具有饱和发生率的捕食者-食饵模型的稳定性及其Hopf分支,讨论了由疾病的潜伏期引起的时滞对种群动力学性态的影响．通过分析特征方程,运用Hurwitz判定定理,讨论了该模型边界平衡点和正平衡点的局部稳定性,并得到了Hopf分支存在的充分条件;通过构造适当的Lyapunov泛函,运用LaSall不变集原理,讨论了该模型边界平衡点和正平衡点的全局稳定性,从而得到了疾病流行而最终形成地方病及消灭的充分条件．     

动态电压振荡型失稳边界分析与算法研究

提出了全参数空间下的最近动态电压振荡型失稳边界的计算方法。在每次迭代中,采用逐步增长负荷的迭代方式找到振荡型失稳边界,求取失稳边界的超平面法向量。将该法向量作为新的负荷增长方式寻找下一步失稳边界,最终找到系统发生电压振荡型失稳的最近边界及其对应的最危险负荷增长方向。相对于摄动方法而言,该方法将各种因素对于电压稳定域的影响考虑在内,且不需要求取控制参数的海森矩阵,具有计算速度快、精度高的特点。选取系统有功负荷作为控制参数,研究了负荷的不同增长方式对系统振荡失稳边界的影响,并根据超平面的法向量求解出系统发生振荡型失稳的最近边界以及所对应的最危险的负荷增长方向。提出2类电压稳定指标,所提指标有助于综合评估系统动态电压稳定裕度。采用3节点和IEEE 14节点仿真系统对算法的有效性进行了验证。     

Prediction of dynamic voltage stability status based on Hopf and limit induced bifurcations using extreme learning machine

Evaluation of voltage stability status considering its dynamic boundaries is a key issue for saving global stability of power systems. However, this evaluation is a computationally demanding task and its implementation is very hard (if not impossible) for on-line environments such as dispatching centers of power systems. In this paper, a new viewpoint for the problem based on modeling it as a forecast process is proposed, which can be implemented with a low computation burden for practical power systems. For this purpose, a voltage stability classification model considering Hopf and limit induced bifurcations is proposed and a new forecast strategy to predict voltage stability class label based on the proposed classification is suggested. The suggested forecast strategy is composed of an information theoretic feature selection technique, extreme learning machine (ELM) as the forecast engine and a line search procedure to fine-tune the settings. The effectiveness of the proposed classification model and forecast strategy is extensively illustrated on the New England 39-bus and IEEE 145-bus test systems.