极限环

A predator model with refuge and toxicity is studied. By constructing a suitable Dulac function, it is shown that there is no limit cycle in the first quadrant, thus the globally stability of the equilibrium is proved. Further more, the paper analyzes the influence of refuge, toxicity and harvesting. It is amazing that ① if the death rate of predator is big or the harvesting effort is big, the existence of the predator is unrelated with refuge; if the death rate of predator and the harvesting effort are small, and the refuge is small enough, the population of both species is increased as the increase of refuge;② if d2=0, the increase of d1 has no influence on the prey population, while the population of predator is decreased.

研究一类有避难所、毒素作用和外界捕获影响的捕食系统，通过构造恰当的Dulac函数，证明系统在第一象限没有极限环，从而证明了平衡点的全局稳定性；分析了避难所、毒素、捕获作用对该系统最终种群数量的影响，发现：①当捕食者的死亡率大或其被捕获得多时，两种群的绝灭与避难所的存在无关；当捕食者的死亡率小、被捕获得多且避难所足够小时，随着食饵避难所的增加，捕食者种群数量也随之增加；②当毒素d2=0时，毒素d1的增加对食饵种群最终数量没有影响，而使捕食者种群数量下降。

When the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulac function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.

选取适当的Dulac函数，利用Bendixson-Dulac判别法证明了极限环的不存在性，说明局部渐近稳定的病虫害平衡点也全局渐近稳定。

In this paper,the existence and stability of fixed points are studied to a Nonlinear Evolution Equation and the nonexistence of limit cycles is proved by the Bendixon-Dulax.

研究了一个非线性发展方程不动点的存在性及其稳定性，并运用Bendixon-Dulax判别法证明了此方程极限环的不存在性

By applying Bendixson-Dulac theroem, we show that the system admits no limit cycle in the first quadrant, thus the global stability of the interior equilibrium is followed.

首先通过运用Bendixson-Dulac定理证明了系统在第一象限没有极限环，从而证明了正平衡点的全局稳定性。

Diffusion problem of a predator-prey model with Holling typeⅡfunctional capturing function is studied. Stability condition is obtained when diffusion is absent, and the effect on stability of positive equilibrium is studied when diffusion is present. In the end, the problem of existence of limit cycle is proved in the first quadrant when diffusion is absent.

针对一类具有HollingⅡ型功能捕获函数的捕食－食饵模型的扩散问题进行了研究，得到了无扩散时正平衡点的稳定条件，以及扩散存在时对正平衡点稳定性产生的影响，最后证明了无扩散时系统在第一象限存在极限环的问题。

Some sufficient condition to guarantee the existence of global invariant manifold s consisting zero homotopic closed orbits is gived.

当在每个不变柱面上有奇点时证明了这类系统局部极限环的存在性；同时给出了这类系统存在由第一类闭轨组成的全局不变流形的条

This thesis is devoted to singular point quantities and integrability conditions of complex polynomial differential systems with resonant singular point, and center-focus determination and bifurcation of limit cycles of planar polynomial differential systems.

在第二章中，对具p∶-q共振奇点的复自治多项式微分系统引入广义奇点量的概念，它是文[103]中奇点量概念的推广，它以在实平面多项式微分系统的中心焦点判断与极限环分支中有着极为重要意义的焦点量和鞍点量作为特例。

The Langford system, which is the same as the Chen and Chua\'s system in being 3D system but different from them in amplitude control application, can be controlled in amplitude of limit cycle directly and effectively and the control gains can be optimized conveniently.

不同于对Chen系统和Chua系统的幅值控制，对于同样是三维的Langford系统，其极限环的幅值控制更加直接而有效，便于实现控制增益的优化设计，而且，对于给定的幅值控制目标，可直接针对原系统进行控制器设计。

The controller employed in the original Langford system can be directly designed for a desirable amplitude target and the exact solutions for amplitudes of limit cycles in systems under some special controllers can be obtained.

此外还设计了一些特殊的控制器，在这些控制器作用下，能够写出受控系统极限环幅值与控制增益之间的精确解析关系。

In favour of arc length algorithm, the curve of fix points of balanced rotor to rotor speed, harmonious and subharmonious unbalance reponse curves are given. The Hopf bifurcation of balance rotor is computed by use of extent equation method.

同时应用扩展方程方法计算了平衡转子的Hopf分叉点，并用求得的Hopf分叉点参数进行数字仿真，证明极限环的存在，因此说明Hopf分叉点的计算是正确的。

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。