渐近稳定的

Using Floquet theory and small amplitude perturbation method, we prove thatthe microorganism-eradication periodic solution is asymptotically stable if the impulsive periodsatisfies some conditions.

利用Floquet理论和小振幅干扰的方法证明脉冲周期满足一定条件时，微生物灭绝周期解是渐近稳定的。

By the corollary to Theorem 4.3, the origin is asymptotically stable.

根据定理4.3的推论，原点是渐近稳定的。

It is proved that there is no limit cycle around the positive equilibra by constructing Dulac function, thus global asymptotic stability of the positive equilibria is proved in the first quadrant.

分析了该系统的平衡点性态，利用Dulac函数证明了系统在正平衡点外围不存在极限环，从而证明了正平衡点在第一象限内是全局渐近稳定的。

Based on it, another sufficient condition on asymptotic stability undering the meaning of Lyapunov's is obtained via the method of equivalent transformation and equivalent system.

在此条件基础上，利用等价变换和等价系统的方法，得到了该闭环系统Lyapunov意义下渐近稳定的充分条件。

In this paper, the method of singular Lyapunov function is used to study singular nonlinear systems , the sufficient conditions about its asymptotic stability and the harmonic oscillation theorm for it are given.

本文运用广义李雅普诺夫函数方法研究了一类广义非线性系统，给出了其渐近稳定的判别条件，对相应的周期系统给出了其平稳振荡定理。

In this method, an interim variable is defined by combining one variable of each subsystem. The interim variable is used to construct the sliding-mode function and the total control law can be derived to guarantee the equilibrium point is reachable in finite time. Using LaSalle invariance theorem, it can be proved further that the equilibrium field only includes one equilibrium point and the equilibrium point is asymptotically stable.

该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的。

In particular, our results does not assume any monotonicity condition on / as is customary in the literature.

我们采用Liapunov函数方法或Liapunov泛函方法获得了这些方程的零解一致渐近稳定的几个充分条件。

The paper is regarding a fourth-order rational difference equation, proving that the positive equilibrium point of the equation is globally asymptotically stable.

研究了一个四阶有理差分方程，证明了该方程的正平衡点是全局渐近稳定的。

We show that a supercritical Hopf bifurcation will occur under some conditions by using the density dependent rate in immature prey population as bifurcation parameter. Sufficient conditions which guarantee the uniform persistence and global stability of boundary equilibrium are also obtained.

我们以幼年食饵个体之间的密度制约率作为分支变量得到在一定条件下将出现超临界Hopf分支，并得到了系统一致持续生存和边界平衡点全局渐近稳定的充分条件。

By utilizing Schur complement formula and the related notion of LMI, a series of sufficient conditions are presented, which guarantee the robustly globally uniformlyasymptotic stability of the closed-loop switched system.

利用Schur补公式和线性矩阵不等式的相关概念，给出了闭环切换系统鲁棒全局一致渐近稳定的一系列充分条件。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。