查询词典 bifurcation

In condensed matter physics,we present an analyticaltopological current theory of point defects which unifies the topologicalquantization,homotopic classification and evolution of defects in oneframework.The number of possible branch lines is shown to be 2s once atmost at the bifurcation point of order parameter with degeneracy s and thetopological charge is conserved during bifurcation processes.

论文在凝聚态物理中给出了缺陷解析的拓扑流理论，将缺陷的拓扑量子化，同伦分类和演化统一在一个框架之内，并证明了在序参量退化度为s的分岔点，缺陷分岔数目最多为2的s次方，而且在分岔过程中拓扑荷是守恒的。

In particular, the system generates bifurcation when 2c-a=0, and then the stable knot bifurcates a hyperbolic saddle point and stable convergence, which is so-called Pitchfork bifurcation. From 2c-a≤0 to 2c-a≥0, the attracting set A of the system is changed from single point to the union set of two different old orbits.

系统在2c-a=0时产生分岔，其稳定的结点分岔出一双曲鞍点和两个稳定的汇，这就是Pitchfork分岔，可见在2c-a≤0变化到2c-a≥0时，吸引集A从单点集变成为连接P和P的两异宿轨道的并。

The first and secondary Hopf bifurcation and the chaos motion of the Langford system are controlled and the relationships between bifurcation parameter and control gains are obtained.

本文分别对Langford系统的一次Hopf分岔、二次Hopf分岔及其混沌运动的控制进行了研究，分别得到控制增益与分岔参数之间的解析关系。

The critical value of Hopf bifurcation was calculated, and the stability of the limit cycle was discussed. The bifurcation diagram of the system was obtained by the fourth order Runge-Kutta method.

定性分析了系统定态的存在性和稳定性，讨论了系统的Hopf分岔，得到了系统的Hopf分岔参数值，并判断了极限环的稳定性。

By the analysis of the difference in the board before the Second Congress of the RSDLP, as well as the bifurcation between Martov and Lenin on the congress, I think the reason for Menshevik"s foundation is not their bifurcation on the problem of party member, but the difference between Martov and Lenin on the election of the RSDLP"s Central Committee and the editorial board of Iskra.

通过分析俄国社会民主工党第二次代表大会之前《火星报》编委会的分裂，代表大会上马尔托夫与列宁的政见分歧，本文认为孟什维克的形成是马尔托夫与列宁在俄国社会民主工党中央委员会和《火星报》新编委会选举上的分歧造成的，而不是我们通常所认为的在党员资格上的分歧造成的。

It is proved that if the RungeKutta method and the linear multistep method are of order p, then the numerical Hopf bifurcation value is an approximation to the Hopf bifurcation value of the equation itself of the same order p.

证明了如果Runge-Kutta方法和线性多步法是p阶的，那么数值Hopf分支值以相同的阶数p逼近于方程本身的Hopf分支值。

The birth rate of the population is assumed to be a bifurcation parameter and nontrivial nonnegative steady-state solution bifurcated from the trivial steady-state solution has been obtained with the bifurcation theory.

应用分歧理论讨论一类单种群模型的非负定态解，并对该解的稳定性进行了分析。

By using center manifold theorem and normal form of maps, we also present formal proofs of the supercritical flip bifurcation at the bifurcation point. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behavior of the single species model with birth pulses are very complex.

利用单参数族映射的中心流形定理、正规型和指数积分函数的性质，得到了具非线性出生率或具密度依赖成熟率的混杂矩阵模型正平衡态的存在性和稳定性、超临界分支以及各种复杂现象甚至混沌。

The grazing bifurcation point is found in terms of the conditions for the existence of grazing orbit.The bifurcation diagrams are gained through previous piecewise smooth map and numerical calculation,they are similar structurally.

利用擦边分岔条件找到了此系统的擦边分岔点，利用推导的擦边分岔的分段映射和直接数值仿真获得不连续分岔图，两者得到的分岔图在结构上是类似的。

The main work of the thesis is summarized as follows:(1) The pitchfork bifurcation of a bidirectional associative memory neural network with three neurons is considered. The pitchfork bifurcation curve can be obtained.

本文主要研究工作如下：(1)研究了含三个神经元的BAM神经网络模型的Pitchfork分支问题，得到了一条Pitchfork分支曲线，并给出了分支曲线图。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。