查询词典 bifurcations

For the first time, we have applied this method to study the problem of bifurcations of map, including codimension one, codimension two and flip bifurcations.

本文将该方法推广至映射分叉问题的研究，包括余维一、余维二分叉和倍化分叉。

The emphasis was placed on the bifurcation problem of impact vibration systems, including codimension one and two bifurcations, flip bifurcations and Hopf bifurcations.

本文着重研究碰撞振动系统的分叉问题，包括余维一分叉、余维二分叉、倍化分叉和Hopf分叉等。

Then we use theory ofnormal form and universal unfolding and Melnikov's and Petrov's methods to studydegenerate bifurcations of codimension three and global bifurcations in the averagedequations.

然后利用规范形理论、普适开折理论、Petrov方法和Melnikov方法研究了平均系统的余维3退化分岔和全局分岔。

First we use the method of multiple scales tostudy local bifurcations of this system and obtain transition sets and bifurcating responsecurves.Then we use theory of normal form and universal unfolding and Melnikov'smethod to study further degenerate bifurcations of codimension two and globalbifurcations.

然后利用规范形理论、普适开折理论和Melnikov方法进一步研究了余维2退化分岔和全局分岔，并且获得了一些有意义的结果，提出了不完全普适开折的问题。

7The local and global bifurcations and degenerate bifurcations of codimension threefor a nonlinear oscillator under combined parametric and forcing excitations are studiedin detail.

7研究了参数激励与强迫激励联合作用下非线性振子的局部分岔、余维3退化分岔和全局分岔。

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

The evolvement and mechanism of border-collision bifurcations and chaos were analyzed after the collision border line was studied. Results show the limitation of duty cycle is the fundamental cause of non-smooth bifurcations.

分析边界碰撞分岔和混沌演化过程及其产生机理，推导出碰撞边界线的解析表达式，指出发生边界碰撞的根本原因在于开关变换器占空比的有界性。

In this thesis,the voltage stability boundary is the combined boundary which correspond to Saddle-node bifurcations and Hopf bifurcations.The closest Hopf bifurcation point is found through the proposed iterative method under the assumption that the Hopf hypersurface is continuous and convex.

因此在本论文中，在多维参数空间下，将稳定边界推广到鞍点和Hopf分岔点构成的混合稳定边界，探索性寻求Hopf分岔超平面的法向量，采用迭代算法求取系统发生最近振荡型电压失稳的负荷增长方式。

A class of fast-scale bifurcations appearing around the maximum value of the input voltage is discovered for the first time by experiment. Then the influence of the fast-scale bifurcations on the performance of the PFC converters is discussed. Whether the fast-scale bifurcations will appear and how wide the bifurcation region depend on the characteristics of the current loop output. Therefore, the main factors that affect the current loop output are analyzed, including the current loop parameters, inductance, and root-mean-square value of the input voltage.

通过实验，该文首次发现了一类在输入电压最大值附近发生的快时标分岔；详细讨论了快时标分岔对PFC变换器性能的影响；由于电流环输出的特点决定了变换器是否会出现快时标分岔以及分岔区域的大小，该文分析了影响电流环输出的主要因素，包括电流环参数、电感值和输入电压有效值。

According to this algorithm, it is shown that the bifurcated periodic solutions through Hopf bifurcations at the first critical value of delay are orbitally asymptotically stable on the center manifold and the bifurcated periodic solutions through Hopf bifurcations at other critical values of delay are unstable.

根据这一算法，发现在时滞的第一个临界值处通过Hopf分支产生的周期解在中心流形上是轨道渐近稳定的，而在其它临界值处通过Hopf分支产生的周期解在中心流形上是不稳定的。

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