查询词典 bifurcation

We study cuspidal loop bifurcation、 Homoclinic or double Homoclinic bifurcation、 Hopf bifurcation and obtain the necessary conditions to generate limit cycles by using the coefficients of the expansion of the first Melnikov function.

利用一阶Melnikov函数的展开式的系数研究了尖点环分支、同宿分支、双同宿分支和Hopf分支，并给出了产生极限环的充分条件。

The researchers in the past only considered the existence conditions of the spatially homogeneous periodic solutions of the kind of models, and regarding the delay or the diffusion rate as a bifurcation parameter, the existence conditions of Hopf bifurcation, and the direction of Hopf bifurcation with Neumann boundary condition.

以前的研究者只讨论了此类系统的空间齐次周期解的存在性条件，或是以时滞，或扩散系数为分支参数的Hopf分支存在的条件，以及Neumann边界条件下此类系统的Hopf分支方向。

Besides, the pitchfork bifurcation of this system is investigated. The pitchfork bifurcation curve can be obtained and the stability of equilibrium points is discussed in the domain partitioned by bifurcation curve.

同时还研究了含有n＋1个神经元的多时滞BAM神经网络模型的Pitchfork分支问题，得到了Pitchfork分支曲线，讨论了在分支曲线的不同区域里平衡点的稳定性。

According to static stability and avoiding the singularity induced bifurcation, saddle-node bifurcation, and Hopf bifurcation in power systems, this paper presents mathematical models for stability equilibrium solutions based on the semismooth property of spectral functions in mathematics.

针对电力系统中静态稳定和避免奇异诱导分岔、Saddle-Node分岔、Hopf分岔几类典型的系统稳定问题，基于数学上谱函数的半光滑特性，建立了系统稳定平衡解的数学模型。

The cavitated bifurcation equation that describes cavity formation and growth in the interior of the sphere is obtained. It is proved that there exists a unique bifurcation point on the trivial solution of the cavitated bifurcation equation.

本文利用分岔理论和动力学理论中的基本观点、方法和结论，对具有缺陷的超弹性材科组成的球体内部的空穴生成和增长的拟静态问题以及空穴生成后随时间的运动规律等方面进行了系统的研究，得到了一些新的结论，同时给出了相应的数值分析。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

The study of Hopf bifurcation includes determining the bifurcation value, the direction of bifurcation and the stability of bifurcating periodic solution.

对系统Hopf分支的研究包括分支参数值、分支方向、分支周期解的稳定性的确定等内容。

Stability of solutions of the cavitated bifurcation equation is discussed in each region by using the minimal potential principle, and the catastrophic phenomenon of cavity formation is explained. 2. In Chapter 4, problems of cavitated bifurcation for two spheres, which are composed of two different kinds of imperfect compressible hyper-elastic materials, were examined, respectively. The parametric analytic solutions of the radially deformed function and the parametric cavitated bifurcation solutions are all obtained for the two spheres.

利用奇点理论给出了空穴分岔方程在分岔点的等价正规形，将缺陷参数分成若干个区域，证明了当缺陷参数属于某些区域时，具有缺陷的超弹性材料球体发生空穴分岔时的临界载荷比无缺陷的小；并利用最小势能原理讨论了空穴分岔方程的解在各个参数区域内的稳定性，解释了空穴生成的突变现象。

In this thesis, we describe some important properties of the dynamic behaviors of several class of time-discrete models of two neurons, which includes stability, asymptotic stability, the existence and attractability of periodic solutions, Flip-bifurcation and Neimark-Sacker-bifurcation.

本学位论文对几类二元离散神经网络模型的动力学性态进行了定性分析，讨论了这些神经网络模型的稳定性、渐近稳定性、周期解的存在吸引性、Flip-分岔和Neimark-Sacker-分岔，全文共分五章。

In this thesis, we describe some important properties of the dynamic behaviors of several class of time-discrete models of two neurons, which includes stability, asymptotic stability, the existence and attractability of periodic solutions, Flip-bifurcation and Neimark-Sacher-bifurcation.

本学位论文对几类二元离散神经网络模型的动力学性态进行了定性分析，讨论了这些神经网络模型的稳定性、渐近稳定性、周期解的存在吸引性、Flip-分岔和Neimark-Sacker-分岔，全文共分五章。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。