极限环

The dynamic stability of this system is discussed by the Hopf bifurcation theory and the condition of the limit cycle occurring is given.

应用Hopf分岔理论讨论了时滞动力系统动态稳定性，给出了系统产生极限环的条件，最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响。

For a 3D system, formulae for a general polynomial controller applied to the normal form of a system and for the relvant stability index are derived. Thereby the amplitude approximation in terms of control gains of the controlled system is solved.

对于三维系统，研究了作用于标准型下系统的普适的多项式控制器设计以及相应的极限环稳定性指标的计算，建立了受控系统的极限环幅值与控制增益之间的近似解析关系。

The second part, the inexistence of limit cycle around o(0,0) about the singularity of the system is perfectly studied with limit cycle theory.

第二部分，运用极限环理论，对系统的奇点o(0，0)外围的极限环的不存在性进行了较完整的分析。

We obtain that:the system has no limit cycle around o(0,0) with the time when o(0,0) is two order of fine focus.we also get some conclusions of inexistence.

得到o(0，0)为二阶细焦点时系统不存在极限环；并且得到了系统不存在极限环的一些条件。

In this paper, a class of dynamical system in biochemistry reaction is discussed by using the method of qualitative analysis. And, at the same time,the existence, nonexistence and uniqueness of a limit cycle are proved, so that the entire results for the system is obtained.

研究微分方程定性理论的应用，利用定性分析的方法，讨论了一类在生化反应中的动力系统，证明了其极限环的存在性、不存在性及极限环的存在唯一性，从而得到了完整的结果。

Results The necessary and sufficient condition of the existence and uniqueness of the limit cycles in this system is completely solved, and then the variance of limit cycle as the changing of parameter is discussed.

结果 得到了该系统存在惟一极限环的充要条件，并讨论了极限环随参数变化的情况。

Using the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given.

对一类三次系统给出了计算无穷远点奇点量的递推公式，并在计算机上用计算机代数系统Mathematica推导出该系统无穷远点的前6个奇点量，进而导出了无穷远点成为中心和最高阶细焦点的条件，在此基础上得到了一个三次系统在无穷远点分支出6个极限环的实例，指出了极限环的精确位置。

In chapter 3,we dig out two families of invariant quartic curves of a quadratic system.

第五章讨论向量场具有对称中心的二次系统，利用系统的不变双曲线及不变四次曲线，我们确定了一个对应极限环（1.1）分布的二维参数区域，其边界的构成为如下几种常见的极限环分枝：霍夫分析，庞加莱分枝，同宿分枝和异宿分枝。

At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated.

第二章研究了一类三次多项式系统由细焦点分支出极限环的问题，证明了该系统有12个小振幅极限环，证明过程是符号和代数的，且焦点量的表达式相对简单。

In the region upstream of vortex breakdown, the sectional streamlines emanating from the leading edge spiral inward to primary vortex and in the region downstream of the breakdown, on the other hand, the streamlines separating from the leading edge are not entrained into the vortex core in the instantaneous sense. Along the axis, the topology of the primary vortex alters several times starting from stable focus near the apex to unstable focus, and lasts back to stable focus near wake edge, the stable hmit cycle and unstable limit cycle are shown in this evolution.

发现在截面流线谱中，即使奇点的类型、数目及位置相同，奇点的连接方式也有可能不同；旋涡破裂点前，主涡由来自前缘的力线卷绕而成，主涡焦点与前缘半鞍点相连，旋涡破裂后，来自前缘的力线不再卷入主涡，主涡焦点与对称面上的鞍点相连：在流体由翼尖流向后缘的过程中，截面流线谱的拓扑结构发生了多次变化，主涡焦点相继由稳定状态转变为不稳定状态，最后又转化为稳定状态，并先后出现了稳定的极限环及不稳定极限环。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。