查询词典 bifurcation

We show that a supercritical Hopf bifurcation will occur under some conditions by using the density dependent rate in immature prey population as bifurcation parameter. Sufficient conditions which guarantee the uniform persistence and global stability of boundary equilibrium are also obtained.

我们以幼年食饵个体之间的密度制约率作为分支变量得到在一定条件下将出现超临界Hopf分支，并得到了系统一致持续生存和边界平衡点全局渐近稳定的充分条件。

Further, the bifurcation diagram and the contour maps of vertical velocity field, streamlines, temperature field, concentration field and sideview shadowgraph intensities corresponding to the convection patterns of three Rayleigh numbers along the bifurcation upper branch were given.

进一步，我们给出了分叉曲线及其沿分叉曲线的上部分支三个Rayleigh数对应的对流图案的垂直速度场，流线，温度场，浓度场和Shadowgraph强度的等值线图。

This is a simple pendulum model of the bifurcation behavior of the bifurcation diagram, is my collection, for your reference.

详细说明：这是一个单摆模型的分岔行为的分岔图，是我珍藏的，供大家参考。

Secondly, the existence of chaos in a special class of discrete-time neural network models with sinusoidal activation function in the sense of Devaney with some parameters of the systems entering some regions are rigorously presented by means of anti-integrable limit method. Whats more, period-doubling bifurcation and saddle-node bifurcation in the neuron model are studied.

其次，利用反向可积极限方法证明了一类周期输入输出函数的离散神经网络模型在参数达到一定范围时产生Devaney意义下的混沌，并讨论了其一维情形的神经元模型出现倍周期分支和鞍-结点分支的情况。

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。

From LS method and singularity theory GS normal form of the circuit bifurcation solution is obtained, and that noly one circuit solution curve exists near bifurcation point is proved.

利用LS约化方法和奇异性理论，导出了非线性电路解分岔的GS范式，证明了电路转折分岔解附近只有唯一一条解曲线。

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。

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