查询词典 bifurcation theory

In this thesis,we consider the problem basing on the Picard-Fuchs equationand bifurcation theory,also using known methods and techniques.We establish therelationship between the number of zeros of the Abelian integral and the number ofintersection points of the"centroid curve"with any straight line.

本文以Picard-Fuchs方程和分岔理论为基础，充分利用已有的方法和技巧，把对Abel积分零点个数的研究转化为对"质心曲线"和任意直线交点个数的研究。

Based on first order ODE approximation theory and Hopf bifurcation theory, the nonlinear motion stability of the train is studied emphatically.

基于常微分方程的一次近似理论和Hopf分叉理论，重点研究了列车系统的非线性运动稳定性。

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论，研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性，其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

In chapter 3,the bifurcation theory of topological current is established inthe neighborhoods of limit point,bifurcation point and higher degeneratedpoint respectively.

第三章讨论和建立了拓扑流在极限点，分岔点和高阶退化点的分歧理论。

By local bifurcation theory and perturbation theory,the existence of local bifurcating solution and its stability are obtained.

研究了一类带简化的Mound-Haldane反应项的捕食-食铒模型的局部共存解存在性及其稳定性，运用局部分歧理论及特征值扰动理论，得到了该模型的局部分歧解存在的充分条件及其解的稳定性。

The bifurcation theory of the plane polynomial vector fields is one important research domain of the theory of ordinary differential equation.

平面多项式向量场的分岔理论是常微分方程定性理论的重要研究领域之一，主要研究依赖于参数的向量场的全局轨线拓扑结构随参数变化的规律。

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。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

The main research work involves:(1) Based on first order ODE approximation theory and Hopf bifurcation theory, the nonlinear motion stability of the train is studied emphatically.

2利用模型A和模型B研究了车辆系统的非线性运动稳定性，利用模型E和模型F研究了列车系统的非线性运动稳定性。

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。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。