The proofs rely on bifurcation theory.
该证明依靠分岔理论。
Bifurcation theory is a useful mathematic method in studying nonlinear system.
分歧理论是研究非线性系统的一种有效的数学工具。
With the aid of bifurcation theory, the theoretical bifurcation condition is derived.
给出了分叉发生的临界条件。
Methods Using the theorem of center manifold and bifurcation theory of planar system.
方法利用中心流形定理并结合平面系统的分支理论。
Firstly, the application of bifurcation theory to the analysis of voltage stability is introduced.
首先介绍了分岔理论在电压稳定性分析中的应用。
Further, the existence of a nontrivial periodic solution is considered by using bifurcation theory.
利用分支理论分析了非平凡周期解的存在性。
The problem of applying bifurcation theory in influence of reactive power compensation upon voltage stability etc.
分析研究了分叉理论应用于无功补偿对电压稳定性影响等问题。
In this paper, spherically symmetric structures of the Brusselator are calculated in detail by using the bifurcation theory.
本文利用分支点理论详细地计算了布鲁塞尔子的球对称解。
Finally, the correctness and rationalization of the unified discontinuous bifurcation theory is verified by the results of experiment.
通过与实验结果比较，验证了统一非连续分叉理论的合理性和正确性。
The rotor bearing system was investigated using the stability and bifurcation theory for nonlinear dynamic system and the database method.
应用精度高、速度快的非线性油膜力数据库方法及非线性动力系统的稳定性和分叉理论对转子-轴承系统进行了分析。
Based on the catastrophe theory, static bifurcation theory and singularity theory, to research the brittleness problems of complex system.
以突变理论、静态分叉理论、奇异性理论等为基础，对复杂系统的脆性问题进行了深入的研究。
The steady solution and its stability of Nonlinear Schrdinger Equation (NLSE) are studied by means of traveling wave transformation and bifurcation theory.
用行波变换方法和分叉理论研究里非线性薛定谔方程的定常解和定常解的稳定性。
The periodic wave solutions of the generalized CH equation are investigated by using bifurcation theory of differential equations and numerical simulations.
用微分方程分支理论和计算机数值模拟方法研究广义CH方程的周期波解。
The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.
运用分歧理论、固有值的解析摄动理论和渐近展开的方法，获得了共存时间周期解的存在性和稳定性。
The bifurcation of travelling wave solutions for the generalized water wave equations are studied by using the bifurcation theory of planar dynamical systems.
应用动力系统分支理论，研究广义水波方程组行波解的分支。
An interesting problem in the study of bifurcation theory is to determine when two bifurcation problems are equivalent with respect to some group of equivalences.
在什么条件下两个分歧问题关于某一等价群而言是等价的，这在分歧理论研究中是很有意义的。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。
In this thesis, using AUTO97, a general continuation and bifurcation software, the problem of voltage stability in power system based on bifurcation theory is studied.
本文以通用分岔分析软件AUTO 97为工具，应用分岔理论，对电力系统电压稳定性问题进行了研究。
Methods the maximum principle, monotone method, bifurcation theory, the perturbation theorem for linear operators and the stability theorem for bifurcation solutions were used.
方法运用极值原理、上下解方法、分歧理论、线性算子的扰动理论和分歧解的稳定性理论进行研究。
The failure forms of rock materials in axisymmetric compression are studied based on the discontinuous bifurcation theory, and a set of experimental data of marbles are simulated.
采用不连续分叉理论，分析了轴对称状态下岩石材料的破坏形式，并采用一组大理岩的实验结果进行了模拟计算。
The main contents in this course includes: qualitative theory in dynamical system, chaos and its numerical recognition, bifurcation theory, the synchronization and control of chaos.
本课程主要内容包括：动力学系统的定性理论，混沌及其数值识别，分岔理论，混沌的同步与控制。
The results concerning the existence, the uniqueness and the stability of stationary bifurcation solutions have been obtained by the bifurcation theory and topological degree theory.
应用分歧理论及拓扑度理论的方法，得到了定态分歧解的存在性、唯一性及稳定性。
Based on homogeneous model and with the application of nonlinear bifurcation theory, this paper presents prediction of static bifurcation (flow excursion) diagram of two-phase natural circulation.
本文基于均相模型，运用非线性分岔理论，计算预测了两相自然循环系统静态分岔(流量漂移)解图。
By means of lower-upper solutions methods, theory of fixed point indices and local bifurcation theory, the conditions for multiplicity and uniqueness positive solutions of this system was obtained.
运用上下解方法，不动点指数理论，局部分歧理论，得出了该系统存在多个正解或惟一正解的条件，即参数对解的个数有一定影响。
The existence of bounded states and limit sets are concerned in order to explain chaos and turbulence phenomena in quantum field theory. Bifurcation and two critical speeds are discussed.
有界状态和极限集的存在性解释了量子场理论中混沌现象与湍流现象的内涵，并讨论了分歧现象与临界速度。
Finally, all the bifurcation curves are obtained using the singularity theory, which provides theoretical basis for dynamic analysis and design of this kind of systems.
最后，运用奇异性理论得到了系统的全部分岔响应曲线，为这一类系统的动态分析与设计提供了理论依据。
In this article, we propose a parabola approximation to the theory of bifurcation.
本文提出二分岔理论的抛物线近似处理。
The systematic research of illegal possession purpose which is inorder to clarify the confusion, eliminate the bifurcation, and deep the research is important to both theory and practice.
对非法占有目的予以系统研究，以求澄清混乱，消除分歧，将该问题引向深入，无论于理论还是实践，都具有重大意义。
New formulations are on the basis of the theory of the bifurcation and the Jacobi matrix eigenvalue structure analysis incorporating the margin and state index of the voltage stability.
这个模型以电压稳定分析的特征结构分析法和分岔分析法为理论基础，把电压稳定的裕度指标和状态指标相结合加入了无功优化中。
New formulations are on the basis of the theory of the bifurcation and the Jacobi matrix eigenvalue structure analysis incorporating the margin and state index of the voltage stability.
这个模型以电压稳定分析的特征结构分析法和分岔分析法为理论基础，把电压稳定的裕度指标和状态指标相结合加入了无功优化中。
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