查询词典 bifurcations

Then we use above mentioned theory to study degenerate bifurcations of codimension two in nonlinear oscillator under combined parame-tric and forcing excitation. Thereby stability problems with double zero eigenvalues can be solved.

然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉，从而解决了当解具有两个零特征值时解的稳定性问题。

We use the method of multiple scales to study local bifurcations of this system and obtainbifurcating response equation,transition sets and eight different diagrams of bifurcatingresponse curves.We find that some singular points in bifurcation set are codimension twodegenerate.

首先利用多尺度法研究了这个系统的局部分岔问题，得到了分岔响应方程、局部分岔集和8种分岔响应曲线，并且发现在分岔集上有一些奇点是余维2退化的。

Finally we study universal unfoldings correspondingto normal forms for the degenerate bifurcations of codimension two,codimension threeand codimension four.

最后研究了余维2退化、余维3退化和余维4退化分岔情况下相应规范形的普适开折。

Bifurcations of limit cycles of a cubic Kolmogorov s system are investigated at the positive equilibrium point .

研究了一类三次Kolmogorov系统在正平衡点处的极限环分支问题。

The flow state in bifurcations is very complex as one of important problems of hydromechanics. It covers many technical and biomedical applications.

流体在叉管中的流态是流体力学中一个非常复杂的问题，该问题的研究涉及很多技术上和生物医学上的应用。

Bifurcations of Zero Crossings: The isotopy theorem [50], [1] shows that transversal intersections are structur-ally stable, i.e., that "transversal zero-crossings" are structurally stable: their topological properties do not change if the size of the filter is slightly changed.

零相交的叉路：同位定理[50]， [1]表示，横截交叉点结构地是槽枥，即，"横截零相交"结构地是槽枥：他们的拓扑学物产不改变，如果轻微地改变大小过滤器。

About bifurcation theory of plane vector fields, the study on bifurcations of the limit cycle has become an important and popular topic.

就平面向量场的分支理论而言，对于极限环分支的研究已成为人们关注的主要问题。D。

By means of numerical simulations,the authors study bifurcations and chaotic behaviors in nonlinear Mathieu equation .

利用数值仿真的方法，对一类M ath ieu方程—欧拉动弯曲问题进行了研究。

Then the explicit algorithm is derived for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the normal form method and center manifold theorem.

然后，利用中心流形定理和正规型方法，给出了确定分支周期解的分支方向与稳定性的计算公式。

By using center manifold theorem and normal form of maps, we also present formal proofs of the supercritical flip bifurcation at the bifurcation point. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behavior of the single species model with birth pulses are very complex.

利用单参数族映射的中心流形定理、正规型和指数积分函数的性质，得到了具非线性出生率或具密度依赖成熟率的混杂矩阵模型正平衡态的存在性和稳定性、超临界分支以及各种复杂现象甚至混沌。

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