分岔

The picture to keep in mind is the diagrammatic tree of life, with ever dividing, ever spreading branches.

这么说，其实是把生命看成是一棵树，一棵枝条不断分岔不断延展的树。

As to the problem of divergency of conventional power flow method,By using an augment eqution this method can get the exact limit of voltage stability and the whole PV curve without encountering the numerical difficulty of ill-conditioning.

针对常规潮流法在鞍结分岔点附近不收敛，该方法通过增加一维潮流方程，消除了功率极限点附近的雅可比矩阵奇异的现象，获取精确的电压稳定极限和整支PV 曲线。

In Chapter 3, a certain polynomial Hamilton system with 3 degree is given. By elliptic integral formulas, the monotonicity of the periodic orbits of this system is verified.

在众多文章中，讨论次谐轨的分岔都需要一个条件，那就是在同宿轨附近的周期轨是单调的，第三章给出了一个具体的三次平面Hamilton系统，利用椭圆积分公式验证了这个系统的一对同宿轨附近的周期轨的周期是单调的，这包含了三种情况，周期轨在右边同宿轨内部，在左边同宿轨内部以及在整个同宿轨圈外部。

The equational restrictions are power flow equations with load coefficients, the power of all the nodes increase synchronously.

本文以分岔分析法为理论基础，将电压稳定的裕度指标加入到无功优化中，提出了考虑电压稳定裕度的无功优化模型。

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。

This bifurcation can lead to a catastrophic change that may be one mechanism of flashover in the compartment fire.

结果表明，在所建立的室内火灾模型中，系统存在鞍—结分岔结构。

In this paper, the resonances of parametric vibration with forced vibration is analyzed and the bifurcation equation of the system is obtained and the singularity analysis is made.

分析了水轮发电机定子系统的参、强联合共振，求得了稳态响应的分岔方程，进行了奇异性分析，揭示了一些新的规律和现象。

This study shows that a forked bifurcation exists in the simplified nonlinear dynamic model.

研究表明，受压细长杆的非线性动力学模型中存在叉形分岔。

The disorder contained can only cause the complexity in the organization, disorder outside organization has the influence to organization complexity, but it cannot cause the organization the complexity, only if it is absorbed and in the organization, can the disorder constitute the complexity; all nature of the complexity is produced because of the disorder in the organization, if there is no the disorder, the organization has no nature such as fortuitousness, randomness, multiplicity and non-linearity, and it is impossible to appear the perturbation, the fluctuation, emerges with phenomenon such as branch, and cannot change suddenly and evolve.

无序只有包含于组织中才能够导致复杂性，组织外的无序对组织的复杂性产生影响，但它不能导致组织的复杂性，只有被组织吸收，成为组织内的无序，才能构成复杂性。复杂性的所有性质都因包含于组织中的无序而产生。没有无序，组织就没有偶然性、随机性、多样性和非线性等性质，就不可能出现扰动、涨落、涌现和分岔等现象，就不能突变和进化。

Based on rubbing model of a two-disk rotor-stator system with consideration of both rotor and stator dynamics,a numerical integration program is applied to numerical simulation and analysis of the nonlinear dynamics of this system,such as bifurcation,Poincare section map,trajectory of axes,phase trajectory,frequency spectrum diagram and time response.

基于一新型径向-轴向复合碰摩双盘转子-机匣力学模型，利用数值积分和Poincare映射方法，对转子-机匣系统由于径向-轴向碰摩故障导致的非线性动力学行为进行了数值仿真研究，给出了系统响应随转速和偏心量变化的分岔图和一些典型的Poincare截面图、相轨图、轴心轨迹、幅值谱图和时域响应等。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。