分岔的

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。

First,a type of numerical solution is proposed to deal with branchswitching at a simple bifurcation point.

提要 在非线性静分岔问题中，针对多自由度高维问题，本文提出一种通用的计算分岔。。。

Then we use theory ofnormal form and universal unfolding and Melnikov's and Petrov's methods to studydegenerate bifurcations of codimension three and global bifurcations in the averagedequations.

然后利用规范形理论、普适开折理论、Petrov方法和Melnikov方法研究了平均系统的余维3退化分岔和全局分岔。

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。

This paper applied an algebraic criterion to identify Hopf bifurcation for the six-dimensional red blood cell survival model, and analyzed stability of the generated limit circle by using projection method.

本文应用任意阶Hopf分岔代数判据对六阶红细胞存活模型的Hopf分岔点进行判定，同时利用投影法判断是否存在稳定极限环。

The direction and stability of bifurcation are determined by the normal form theory and center manifold theorem. Results of some computer simulations are displayed graphically.

利用中心投影方法我们给出了分岔方向和稳定性的计算公式，并利用计算机对Neimark-Sacker-分岔进行了模拟验证。

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。

It is pointed out that the critical stretch of the sphere composed of the first kind of materials given in this chapter is less than that for the perfect materials. Finally, stability of solutions of the cavitated bifurcation equation is discussed. 3. In Chapter 5, problem of radial motion for a solid sphere composed of an imperfect incompressible hyper-elastic material, subjected to a surface tensile dead load, is examined.

第四章中，分别研究了两类具有缺陷的可压缩超弹性材料球体在表面均布的径向拉伸作用下的空穴分岔问题，得到了两类材料球体的径向变形函数的参数型解析解和参数型空穴分岔解，同时指出了本章中给出的第一种缺陷材料组成的球体与无缺陷材料的相比会提前发生空穴分岔。

The following exciting results are revealed: 1 When considering the influence of some nonlinear elements such as hard-limit of exciters, the effects of some devices such as Power System Stabilizer and Static Var Compensator which can introduce positive damping in power system, the reasonability of system parameter values in simulation, the SNB surface and HB surface on the boundary of SSSR will turn close to each other and even coalesce together; 2 Under some conditions, coupling between slow exciters and shunt capacitors will bring negative damping in power system dynamics, which increases the possibility of oscillatory instability. So the power system with mass shunt compensators is easily subjected to the oscillatory instability. In recent years, chaotic phenomena of power system have been reported many times. Some simulation studies even found chaos existing inside the power system SSSR. In this dissertation, chaotic phenomena in power systems are thoroughly studied in order to make clear the relation of chaos and SSSR. The following results are derived: 1 Based on Li-Yorke Theorem and their definition on the chaos, the existence of chaos in power system is verified; 2 Three possible routes of causing chaos in power system are found and deeply investigated. They are route of cascading period doubling, route of directly initial energizing and route of torus bifurcation (or quasi-periodicity). The latter two routes are investigated for the first time in power system stability studies; 3 When the stability conditions of chaos are broken, it is found they can lead to voltage collapse, angle divergence, or voltage collapse with angle divergence simultaneously.

针对在电力系统小扰动稳定区域内可能存在混沌吸引域的有关报道，本文深入研究了电力系统混沌现象的出现途径和与系统失稳模式之间的关系：1利用Li-Yorke定理和Li-Yorke的混沌定义，从理论上证明了电力系统混沌现象的存在性；2发现了电力系统中导致混沌出现的三种可能途径：倍周期分岔导致混沌、初始能量直接激发混沌和经由环面分岔导致混沌，并对后两种新发现的途径进行了较为细致的研究；3发现了混沌极限环破裂导致电压崩溃、角度失稳以及电压崩溃和角度失稳同时出现的现象，其中混沌极限环破裂导致系统角度失稳和电压崩溃及角度失稳同时出现的现象均属首次报道；4证明由微分-代数方程描述的系统模型，其小扰动稳定域的边界只包含HB、SNB和SIB三种分岔界面，在SSSR的内部和边界上，均不可能存在会导致混沌的点，从而将混沌现象排除在小扰动稳定域的研究之外，简化了后者的研究工作。

Do not gum up the work by telling mother what we are going to do .

别告诉母亲我们要干的事，那会把事情搞糟的。

In recent years, application of the partial prestressed concrete beam s is developed.

近年来，随着部分预应力砼梁应用的推广，发现我国规范所采用的名义拉应力法的计算结果不稳定。