查询词典 bifurcation

It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraints near the critical point by using singularity theory.

用奇点理论证明了，空穴分岔方程在临界点附近等价于具有单边约束条件的正规形。

In Chapter 3, problems of cavitated bifurcation for a solid sphere composed of imperfect incompressible hyper-elastic materials, subjected to a surface tensile dead load, are examined.

证明了空穴分岔方程的平凡解支上存在唯一的分岔点；给出了左分岔和右分岔的判别条件，并指出了向左分岔的空穴分岔解还会发生二次转向点分岔。

The problem of spherical cavitated bifurcation was examined for a class of incompressible generalized neo-Hookean materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations.

[1]上海大学数学系，上海市应用数学和力学研究所，上海200072 [2]上海大学数学系，上海市应用数学和力学研究所，上海200072／／烟台大学数学与信息科学系，山东烟台264005

This paper is devoted to discuss the bifurcation of a chemostat with delay and simplified Holling type-IV response function.

关于培养器模型各种类型的方程如常微分方程，偏微分方程和时滞微分方程等已经有了很多结果。

This thesis mainly investigates the single food chain Chemostat models, analyzing the stability of equilibrium points, the existence and uniqueness of periodic solutions as well as the Hopf bifurcation theorem.

本文主要探讨单食物链微生物培养模型的解的稳定性，周期解的存在性和唯一性以及分支问题。

Numerical analysis is given to discuss the influence of response time and frequency detuning on the characteristics of bifurcation and noise.

以响应时间及频率失调为参变量，对其分岔及噪声等动态行为进行数值分析。

The following exciting results are revealed: 1 When considering the influence of some nonlinear elements such as hard-limit of exciters, the effects of some devices such as Power System Stabilizer and Static Var Compensator which can introduce positive damping in power system, the reasonability of system parameter values in simulation, the SNB surface and HB surface on the boundary of SSSR will turn close to each other and even coalesce together; 2 Under some conditions, coupling between slow exciters and shunt capacitors will bring negative damping in power system dynamics, which increases the possibility of oscillatory instability. So the power system with mass shunt compensators is easily subjected to the oscillatory instability. In recent years, chaotic phenomena of power system have been reported many times. Some simulation studies even found chaos existing inside the power system SSSR. In this dissertation, chaotic phenomena in power systems are thoroughly studied in order to make clear the relation of chaos and SSSR. The following results are derived: 1 Based on Li-Yorke Theorem and their definition on the chaos, the existence of chaos in power system is verified; 2 Three possible routes of causing chaos in power system are found and deeply investigated. They are route of cascading period doubling, route of directly initial energizing and route of torus bifurcation (or quasi-periodicity). The latter two routes are investigated for the first time in power system stability studies; 3 When the stability conditions of chaos are broken, it is found they can lead to voltage collapse, angle divergence, or voltage collapse with angle divergence simultaneously.

针对在电力系统小扰动稳定区域内可能存在混沌吸引域的有关报道，本文深入研究了电力系统混沌现象的出现途径和与系统失稳模式之间的关系：1利用Li-Yorke定理和Li-Yorke的混沌定义，从理论上证明了电力系统混沌现象的存在性；2发现了电力系统中导致混沌出现的三种可能途径：倍周期分岔导致混沌、初始能量直接激发混沌和经由环面分岔导致混沌，并对后两种新发现的途径进行了较为细致的研究；3发现了混沌极限环破裂导致电压崩溃、角度失稳以及电压崩溃和角度失稳同时出现的现象，其中混沌极限环破裂导致系统角度失稳和电压崩溃及角度失稳同时出现的现象均属首次报道；4证明由微分-代数方程描述的系统模型，其小扰动稳定域的边界只包含HB、SNB和SIB三种分岔界面，在SSSR的内部和边界上，均不可能存在会导致混沌的点，从而将混沌现象排除在小扰动稳定域的研究之外，简化了后者的研究工作。

Methods To observe the common carotid artery and its bifurcation, the internal carotid artery, external carotid artery intima-media thickness, plaque echo and hemodynamic changes.

方法观察颈总动脉及其分叉处、颈内动脉、颈外动脉内中膜厚度、斑块回声及血流动力学改变。

Two cases underwent simple tumor excision,two cases underwent combined resection of tumor and external carotid, the other four cases underwent combined resection of tumor and carotid bifurcation.

回顾性分析1983至1997年间我院收治的8例颈动脉体瘤患者的临床资料。2例单纯切除肿瘤，2例合并颈外动脉切除，4例合并颈动脉分歧部切除术。

Methods A total of 125 cases including 40 hypertension patients without LVH, 45 hypertension patients with LVH and 40 control subjects underwent color Doppler ultrasonography. Intima-media thickness, plaque and hemodynamic indices were respectively measured in the common carotid artery and its bifurcation, internal carotid artery and external carotid artery.

对134例受检者进行颈动脉超声研究，其中高血压病非LVH 32例，高血压并LVH 62例，正常对照组40例，分别测量各组颈部动脉总干内中膜厚度、分叉内中膜厚度、斑块以及两侧颈总动脉、颈内动脉、椎动脉的血流动力学指标。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失