查询词典 bifurcating

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

By local bifurcation theory and perturbation theory,the existence of local bifurcating solution and its stability are obtained.

研究了一类带简化的Mound-Haldane反应项的捕食-食铒模型的局部共存解存在性及其稳定性，运用局部分歧理论及特征值扰动理论，得到了该模型的局部分歧解存在的充分条件及其解的稳定性。

Moreover, in the parameter plane determined by some two parameters,we discuss codimension two bifurcations caused by the intersections of two bifurcating curves.

同时，在两个参数确定的半参数平面上，我们通过分岔(来源：46e646ABC论文网www.abclunwen.com)曲线的交点讨论了余维2分岔的存在性，即等变Pitchfork-Hopf分岔和Hopf-Hopf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。

The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained. An example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time.

同时计算出系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件，从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例。

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

The present situation in flood-control and waterlog-drain are analyzed, and the present problems are pointed out.2 The causes and characteristics of the floods in Linyi are summarized, and the flood-control project and the waterlog-drain system in Linyi are also introduced.3 On the basis of summarizing the reconnaissance data of engineering geology, the engineering geology conditions of flood-control projects in the city of Linyi are studied, including the floodway project ,the hinge project, the Ge-Jiu Road Bridge project, the No.327 national highway road bridge project, the E-Huang Road Bridge project, and the Xiaogezhuang's chief inverted siphon project in the project of "Bifurcating the Su River to the Beng River".4 Seepage FEM analyses are carried out on the flood-control projects of Yi River, Beng River and Xiaosu River, respectively.

总结了临沂市洪灾成因及洪水特性，介绍了临沂市城市防洪工程和排涝工程。 3、在综合工程地质勘察资料基础上，分析了临沂市城市防洪工程的工程地质条件，包括："分涑入祊"分洪道工程地质条件分析、"分涑入祊"枢纽工程地质条件分析、"分涑入祊"葛九公路桥工程地质条件分析、"分涑入祊"327国道公路桥工程地质条件分析、"分涑入祊"鹅黄公路桥工程地质条件分析、"分涑入祊"小葛庄总干倒虹吸工程地质条件分析。

First of all, the method of Fredholm alternative is used to obtain the approximate solution of the first order for the bifurcating periodic solutions of a nonlinear system with delayed velocity feedback. The bifurcation direction and the stability of the bifurcating periodic solution are also determined.

首先，用Fredholm择一方法分析了一具有时滞速度反馈的非线性振动系统的Hopf分叉，得到了局部分叉周期解的近似表达式，确定了分叉解的分叉方向及稳定性。

We also refer to the center manifold theorem and normal form theory, and list two calculation formulas which reflect the stability with Hop bifurcating periodic sollution, bifurcating direction.Thus provide a basis for numerical simulation calculation.

我们还用中心流形定理和规范型理论给出了确定Hopf分支周期解的稳定性，分支方向的计算公式，为数值模拟计算提供了依据。

It is shown that the direction of bifurcation and the stability of the bifurcating periodic solutions of the Euler methods are the same as the direction of bifurcation and the stability of the bifurcating periodic solutions of the original delay differential equation when the stepsize is small enough.

证明当步长充分小时数值Hopf分支的分支方向、分支周期解的稳定性与原方程的Hopf分支的分支方向、分支周期解的稳定性相同。

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