平衡点

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。

Firstly, we consider SIQR epidemical models with continuous and pulse vaccinations; the reproduction numbers have been obtained for those models; by using Dulac function, we prove the global stabilities of equilibrium of SIQR model with continuous vaccination. In the SIQR epidemical models with pulse vaccinations, we have also discussed the existence of the infection-free periodic solution, the global stabilities of the infection-free periodic solutions, and the effectiveness of pulse vaccination and continuous vaccination policies has been compared for the two models.

文中首先考虑具有连续免疫接种和脉冲免疫接种的SIQR传染病模型，分别获得了它们各自的基本再生数；利用Dulac函数方法证明了具有连续免疫接种的SIQR模型无病平衡点的全局渐近稳定性；在脉冲免疫接种下SIQR传染病模型里，讨论了无病周期解的存在性，证明了该周期解的全局渐近稳定性，并且对连续和脉冲接种下的SIQR传染病模型的接种效率进行了比较。

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。

The equilibrium point of the network and the eigenvalue is only need to get the result.

所有结果只需计算网络的平衡点与矩阵的特征值。

In section 3, we construct the special function and analysis the functional graph, we study the global periodic solution with only one interior stable point by ejective fixed point theory.

第三节构造特定的函数、分析函数图像，并利用喷射点不动点理论分析该模型只有一个内部平衡点时的大范围周期解问题。

It is a very difficult problem to look for the best equalization point between these two.

在这两者之间寻找最佳平衡点是一个困难的问题。

In addition, the stability of constant positive equilibrium point is discussed by elementary concept and methods in population dynamics.

同时，由种群动力学中的一些基本概念及方法，讨论该模型的常数正平衡点的稳定性。

The aim of this paper is to demonstrate the use of the open loop control to change the nonlinear system parameters in order to obtain a desired equilibrium bifurcation diagram.

利用开环控制来改变非线性系统的分岔参数，使之获得理想的平衡点分岔图。

Then, according to the target of the controller design, the desired equilibrium point of the system is obtained.

然后，根据系统控制器的设计目标，确定了系统期望的平衡点。

Therefore, in the financial innovation should be looking for a relative equilibrium point.

因此，在金融创新应寻求相对的平衡点。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。