分岔的

In the first part,we use adjoint operator method and matrixrepresentation method to compute normal forms of higher order for nonlinear dynamicalsystems with Z2—symmetry and Z2—asymmetry.

在第二部分里，利用多尺度法、规范形理论、普适开折理论、Melnikov方法和Petrov方法分别研究了参数激励作用下非线性振子、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2退化分岔、余维3退化分岔和全局分岔。

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。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

The parameter space is included to construct a compound piecewise smooth map by composing previous discontinuity mappings with a Poincarémap for smooth periodic solution.

引入参数空间，将未发生碰撞的周期轨道对应的光滑映射与前面得到的不连续映射复合得到两类擦边分岔的分段映射形式。

The one who appeared to be their chief held a postilion's whip in his hand.

在大路和那马路的拐角上，也就是在那分岔的地方，他们听到一种在那种时刻很难理解的声音，并且还出现了一群黑压压的模糊形象。

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。

Melnikov method is employed to study the bifurcations and chaos of homoclinic and subharmonic orbits for two pendulum systems.

用Melnikov方法研究具有弱阻尼与参数激励的单摆以及倒摆运动的同宿轨道分岔、次谐分岔和混沌现象，得到了发生同宿轨道分岔、次谐分岔和混沌的临界参数，并将所得理论结果与倒摆运动的实验结果进行了比较与讨论。

The results show that,the control of delaying period-doubling bifurcations and unstable periodic orbits in a chaotic attracter of the AOB system is effectively realized,and other stable periodic orbits 2np、3mp and 2np×3mp are obtained by adjusting the control parameters.

仿真模拟显示，通过选择恰当的控制参数，有效地实现了声光双稳系统中倍周期分岔的延迟控制和混沌吸引子中原不稳定周期轨道的稳定控制，同时，还可以将系统控制在2np、3mp 和2np×3mp这样其它任意所需的周期轨道上。

It is found that under certain conditions stochastic bifurcation mostly occurs when a stochastic attractor collides with a stochastic saddle.

揭示了随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的。

Moreover, scanning tunneling microscopy images of the SWCNT with atomic resolution show that it has a (10, 10) structure with a diameter of 1. 3nm and the current-voltage characteristics in quasi-radical direction reveal its metallic properties.

未经过超声的SWCNTs容易凝聚；观察到纳米管弯曲、分岔的现象，这是由于纳米管的六边形网络中引入五边形、七边形、八边形等缘故；得到（10，10）型SWCNT的原子像；测量了SWCNT的准径向I—V曲线，表现为金属性。

Do not gum up the work by telling mother what we are going to do .

别告诉母亲我们要干的事，那会把事情搞糟的。

In recent years, application of the partial prestressed concrete beam s is developed.

近年来，随着部分预应力砼梁应用的推广，发现我国规范所采用的名义拉应力法的计算结果不稳定。