查询词典 bifurcation theory

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。

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。

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。

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。

Metrorrhagia is also gynaecological problems of common diseases.

崩漏是妇科常见病也是疑难症。

WordFTP gives you the convenience and timesaving you need.

wordftp让您的方便和省时您所需要的。