查询词典 bifurcation point

Comparing with deterministic system, the point of bifurcation in stochastic Duffing-van der Pol system is moved as increasing the intensity of random parameter.

进一步的推广证实正交多项式逼近法在实际问题中有广阔的应用前景，它可以解决含有多个随机参数的非线性随机动力学系统的分岔问题。

In this work, we mainly study the numerical analysis of bifurcation theory, especiallythe numerical computation of Takens-Bogdanov point in delay differential equations.

本文中，我们主要考虑分支理论的数值方法，具体而言，时滞微分方程中Takens-Bogdanov点的数值计算方法。

Double homoclinic loops; Resonant eigenvalues; Nontwist; Periodic orbit; Bifurcation; Periodic solution; Predator-prey system; Fixed point theorem; Coincidence degree; Delay; Functional response function

基础科学，数学，动力系统理论双同宿环；共振特征根；非扭曲；周期轨；分支；周期解；捕食者-食饵系统；不动点定理；重合度；时滞；功能反应函数

Critical point theory;nonlinear elliptic differential and difference equation;existence of solution;multiply results;bifurcation;Trudinger—Moser inequality;applications

论文导师刘三阳，论文学位博士，论文专业应用数学论文单位西安电子科技大学，点击次数 4，论文页数 116页File Size3483K

The curriculum comprises the fundamental concepts of point set topology, differential manifold and differential dynamics, followed by the conceptions and theoretical methods of abrupt change, bifurcation, chaos and fractal. The analysis and compare combined with the practice in power system make it easy for readers to learn the basic methods of nonlinear dynamics and write high quality papers.

本课程主要内容包括点集拓扑学、微分流形和微分动力系统的基本概念，后面部分主要涉及到突变与分叉、混沌、分形和分维概念和理论方法，并结合电力系统实际例子加以分析与比较，使读者很快掌握非线性动力学的基本方法，能够写出高质量的文章和学术论文。

Mainly by means of the Hopf bifurcation theorem and the cone fixed point theorem in the functional differential equations.

本文对非线性项为两种形式的时滞Van der Pol方程分别加以比较，利用Hopf分支理论和锥不动点定理，得到相应方程在周期解和Hopf分支方面上的差异。

This thesis is devoted to the problems of integral conditions, center -focus determination and bifurcation of limit cycles at degeneratesingular point and the infinity of planar polynomial differential system.

本文主要研究平面多项式微分系统退化奇点与无穷远点的可积条件以及中心焦点判定与极限环分支，全文由七章组成。

In Chapter 4, we study the center conditions and the bifurcation of limit cycles at a degenerate singular point as well as that at infinity for a quintic polynomial system and prove that the system has 5 limit cycles around the origin and 2 limit cycles around infinity.

在第三章中，我们分别研究了一类三次多项式系统、一类五次多项式系统、一类七次多项式无穷远点的中心条件与极限环分支问题。

The stability of system equilibrium point and the existence condition of 3-D Hopf bifurcation as well as the stability of hence generated periodic solution were analyzed, so that the existence of limit cycles on the two-dimensional stable manifold of one microbial species and its nutrition was verified when other one had the disadvantage in the competition so as to become extinct.

研究当营养消耗率δ1＝δ1为一般的非减连续函数和δ2＝常数的三维Chemostat模型，分析系统平衡点的稳定性，三维系统经历Hopf分支的条件和由此产生的周期解的德定性，证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养的二维稳定流形上极限环的存在性。

The stability of system equilibrium point and the existence condition of 3-D Hopf bifurcation as well as the stability of hence generated periodic solution were analyzed,so that the existence of limit cycles on the two-dimensional stable manifold of one microbial species and its nutrition was verified when other one had the disadvantage in the competiti.

研究当营养消耗率1δ=1δ为一般的非减连续函数和2δ=常数的三维Chemostat模型，分析系统平衡点的稳定性，三维系统经历Hopf分支的条件和由此产生的周期解的稳定性，证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养的二维稳定流形上极限环的存在性。

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