查询词典 bifurcation point

The study of bifurcation problems is mainly about how to imply the related concepts and techniques in singularity theory of smooth map germs to bifurcation problems.

研究分歧问题主要是如何将光滑映射奇点理论中的相关概念和技巧适当地引到分歧问题中来。

Secondly, method of Taylor series is used to approximate the slow manifold and the O approximation of the slow manifold is given; slow dynamics such as saddle node bifurcation which has been proven to be the same as that for the full system is analyzed; at the same time, fast dynamics including bifurcation conditions and domain of attractor of the stable equilibrium are also analyzed; the attracting region which consists of the stable manifold of the unstable equilibrium and stable equilibrium is given; we found that when the inner flux decay increases, the domain of attractor is enlarged.

首先，给出了电力系统SMIB模型的时间尺度分解，得到标准的奇异摄动模型；其次，利用幂级数方法，给出了慢流形的O近似M〓，分析了在慢流形M〓上的慢动态，得到了慢子系统的鞍结分支值，并证明此分支值与原系统的鞍结分支值相同；分析了快子系统的平衡点和全局分支的存在条件，给出由不稳定平衡点的稳定流形与稳定平衡点形成的吸引域；并研究内部电压对稳定域的影响，发现稳定域随内部电压增加而扩大；最后给出整个系统的稳定平衡点的近似吸引域。

Analog to the discontinuous bifurcation analysis for classic elasto-plastic theory by Ottosen and Runesson et al, the sufficient and necessary conditions of weak discontinuity and strong discontinuity localization bifurcation for the strain-gradient-enhanced-damage model are obtained.

借鉴Ottosen和Runeson等的弹塑性模型不连续局部化分岔方法，对应变梯度损伤模型推导出与梯度相关的强不连续和弱不连续局部化分岔充要条件。

After undergoing a chaotic region, the period number will add one, in the same time, magnitude of the subharmonic response increases in sequence as the rotational speed ratio increases. When the rotational speed is below the critical speed, the chaotic bands resulted directly from a perioddoubling bifurcation occur among the successive orders of superharmonic responses, then they can return directly to periodic motion by a reversed period-doubling bifurcation.

在转速小于临界转速的情况下，在分岔图中各个连续阶亚谐运动的转换区中分别都出现了经由一个倍周期分岔直接导致的混沌频带，后又直接由一个逆倍周期分岔转化为周期一的运动，同时在三个混沌频带之间都出现了幅值突跳的现象。

"We decided to quantify the calcium findings in the aorta and stratify calcium by total score, as well as scores in suprarenal, laminar, and bifurcation segments," Dr. Davila said. In general, the highest calcium scores were found in the laminar area, but "these scores did not correlate with a statistically significant increased risk." By contrast, a total calcium score or bifurcation score above the 75th percentile "correlated with a 10-fold increase in risk of cardiac event," he said.

Davila医师表示，我们决定主动脉钙含量的发现、利用总分来分类钙含量，以及肾脏上方、薄层、分支区段的指数；一般而言，指数最高的位置在於层状区域，但是这些指数与心血管风险的增加之间并没有显著的关连；相反的，总钙含量指数或是分支区段指数高於四分位数前75%者，与增加10倍心血管疾病的风险有关。

By means of singularities theory the transition variety and bifurcation diagram of the bifurcation equation of the system is accuired.

按照奇异性理论方法对分岔方程进行了分析，得到了分岔方程的转迁集和分岔图。

Here,we choose c as a bifurcation parameter,mainly proof transversality condition,such that we discuss the bifurcation problem of traveling-wave solution.

对这类具有旋转对称性的系统问题行波解的相关性质，已有许多学者做了大量的研究工作。

Moreover, the stability of unfoldings of such kind of bifurcation problems is discussed, and the sufficient condition of an unfolding of a bifurcation problem to be stable is that it is versal unfolding under certain conditions.

得到的这种分歧问题的无穷小稳定与稳定是等价的，而且讨论了这种分歧问题开折的稳定性，得到了一定条件下分歧问题开折稳定的充分必要条件为该开折是通用开折。

Analysis of power spectrum indicates that the characteristic frequency created by the Hopf bifurcation is equal to the generalized winding number of the critical transverse modes just before the bifurcation.

结果表明，耦合振子的同步混沌态可以发生一种Hopf分岔，在Hopf分岔后，系统的功率谱中出现了一个特征频率，其值恰好等于分岔前临界横模的广义旋转数。

This condition is weaker than the conditon for complete topological conjugacy of two families of systems, so it is significant and useful for deducing from relatively simple systems or systems with known bifurcation points to the systems with unknown bifurcation points.

这一条件比两族系统完全拓扑共轭弱，因此是有理论意义的，可以使我们从相对较简单的或已知分支点状况的系统来推知未知系统的分支点。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。