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The criterion of the globally asymptotic stability of equilibrium point is given via the method of constructing a suitable Lyapunov functional and sector condition.

通过构造适当的Lyapunov泛函及扇区条件,给出了平衡点渐近稳定的判定准则。

By constructing suitable Lyapunov functions, we establish sufficient criteria for asymptotic stability of the zero solutions.

利用构造Lyapunov函数的方法,给出了零解的渐近稳定的充分条件。

In this paper,by using the comparison theorems and constructing suitable Lyapunov function, the sufficient conditions are obtained for the permanence and existence of globally asymptotically stable positive periodic solution of the system.

研究了具有反馈控制的n种群非自治周期竞争系统的持续性,利用微分不等式并构造适当的Lyapunov函数得到系统存在惟一、全局吸引的正周期解的充分条

This paper consists of three parts:We first consider the non-autonomous predator-prey system with both Beddirigton-DeAngelis functional response and dispersion. By using comparison theorem of differential equation, we study the permanance of the system. After that, by constructing suitable Lyapunov function, we obtain some sufficient condition which guarantee the existence of globally asymptotically stable almost periodic solution of the system.

本文研究三方面的内容:第一部分考虑具有扩散和Beddington—DeAngelis功能反应的捕食-食饵系统,利用微分方程比较原理得到该系统一致持续生存的条件;通过构造适当的Lyapunov函数得到了该系统存在全局渐近稳定概周期解的充分条件。

With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution. Finally, we study a multispecies predator-prey system with stage structure and Holling II type functional response.

第二部分考虑具有阶段结构的非自治扩散捕食系统,利用比较定理得到该系统持久生存的充分条件,其后在概周期情形下通过构造合适的Liapunov函数得到了保证该系统存在唯一一个全局渐近稳定的概周期解的条件。

We prove uniform persistence and global attractability bythe comparable theory and constructing Lyapunov function method.

本文第三章中,提出了既具有反馈控制项,又有扩散项和α_i类功能性反应函数的n种群非自治Lotka-Volterra竞争生态系统。

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论,研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性,其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

Then by using the Riemann's function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数,通过构造辅助问题,得到了一个等价积分微分方程。

Then by using the Riemanns function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数,通过构造辅助问题,得到了一个等价积分微分方程。

Aiming at a class of typical dynamic hysteretic models, a kind of sliding mode tracking controller based on dynamic sliding mode principle is proposed. A dual-phase convergent process is implemented by constructing an auxiliary sliding mode variable.

针对一种典型的动态迟滞模型,提出一种基于动态滑模原理的跟踪控制器,通过构造辅助的滑模变量来实现动态滑模控制的两阶段收敛。

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