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In this paper , for a co-dimension two-bifurcation system that is on a three-dimensional central manifold and subjected to a parametric excitation by a white noise , the asymptotic expansion of the maximal Lyapunov exponent is evaluated.

为了分析白噪声参数激励对三维中心流形上一类余维2分岔系统的影响，本文基于一维扩散过程的奇异点理论，通过使用 L。

As an application of our method, we solve the problems of center conditions and bifurcation of limit cycles at infinity for a quintic polynomial system.

作为应用，我们在复域中详细地求出了一类五次多项式系统的原点成为中心、拟等时中心的条件。

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论，研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性，其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

Firstly, The sufficient con-ditions of the existence and uniquity of the positive equlibria by applying functional derivative isobtained; Secondly, the global attractability of the positive equlibria is investigated by charateristicroots theory and oscillation theory; Thirdly, regarding the delay as a parameter, conditions of theexistence of Hopf bifurcation and the peridic solution, furthermore, the form of the approximateperidic solution are obtained; Finally, Some specific examples are given and the solution diagrameappears by Matlab.

首先利用导数性质，得到了该模型正平衡态存在惟一性的充分条件；其次，利用特征值和振动性理论得到了该模型正平衡态全局渐近稳定性充分条件；然后，应用Hopf分支理论证明了该模型Hopf分支及近似分支周期解的存在性，并给出了周期解的近似表达式；最后，借助于MATLAB数学软件，举例并绘出了模型数值解的拟合图象，验证了文中定理条件的可行性。

In this thesis, the limit cycles bifurcated from some kinds of polynomial systems are investigated using the methods of bifurcation theory and qualitative analysis.

本文利用分支理论和定性分析的方法，借助于计算机等辅助工具对几类多项式系统的极限环分支问题进行了研究。

First,a type of numerical solution is proposed to deal with branchswitching at a simple bifurcation point.

提要 在非线性静分岔问题中，针对多自由度高维问题，本文提出一种通用的计算分岔。。。

Experimental study on the Hopf bifurcation characteristic of single point mooring vessels is presented.

对单点系泊船舶的Hopf分岔现象进行了试验研究。

A periodic oscillation analytic solution for the system at bifurcation point was obtained by using the method of series.

利用级数法求出了系统在分歧点处的时间周期振荡解的解析表达式。

This theory can be used to find the bifurcation point on the equilibrium path and obtain the critical load and critical mode.

采用了塑性增量理论来决定结构的塑性应力状态，避免了结构反应对加载路径强烈的依赖性。

At the bifurcation point, the max amplitude of the system varies intensely.

在周期解分叉点上系统的最大振动幅度都发生明显的变化。

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