查询词典 bifurcation

This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.

这表明，仅采用Casson模型模拟整个颈动脉流场是不合适的，而牛顿流体则是描述血液在颈动脉分岔血管中流动的一个很好的近似。

However, the Casson equation agrees well only when the shear rate is less than 10 s?1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation.

然而Casson模型只有在低切变率条件下才与血液吻合的较好，而在颈动脉分岔血管中切变率值的分布范围却很广，因此，我们有理由认为，在整个颈动脉分岔血管流场中均采用Casson模型来模拟血液的本构关系是不够的。

The deterministic neuronal firing model could simulate only the period adding bifurcation scenario in which period n bursting was changed into period n+1 bursting directly. The period adding bifurcation scenario and the new firing pattern similar to the experiment could be simulated in the stochastic Chay model.

确定性神经放电理论模型只能模拟周期n节律直接到周期n+1节律的加周期分岔序列；而随机Chay模型可以模拟实验中的加周期分岔过程和新节律。

Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case.

另外还证明：关于频率的分岔问题具有无穷余维，因此该情形下的动力学分岔行为非常复杂。

It is found that a codimension 2 bifurcation can be produced by a constant treatment rate, and a backward bifurcation occurs due to a nonlinear treatment rate.

发现了常数治愈率引起余维2分枝，非线性治愈率导致后向分枝，比较了标准发生率和双线性发生率对传染病演变趋势的影响。

The loca l bifurcation characteristic near by codimension two bifurcation point is discus sed,which testifies that the local dynamical behavior of map fmay be known under the condition of cod.

通过分析范式在余维二分岔点附近的局部分岔行为，可以了解映射f在余维二分岔条件下的局部动力学行

In this paper,we study the bifurcation theory of reaction diffusion equation,we give a rigorous bifurcation analysis for a reactor model with combination of quadratic and cubic steps.

在无差速流动反应扩散模型的讨论中，对有二次项和三次项的反应模型的分歧解给出了严密的分析。

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

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。

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