| 1. | Conditions for permanence is established via the method of comparison involving multiple liapunov functions
进而，利用李雅普诺夫函数和比较定理确定了持续生存的条件。 |
| 2. | Furthermore , according to the method of liapunov functions in the stability theory , both the globally asymptotic stability and the attractive regions of the nonnegative equilibrium in the model are discussed
同时，对系统解的吸引域以及平衡态的全局稳定性，采用李雅普诺夫函数法进行完整的讨论。 |
| 3. | In the fourth part , we structure liapunov function to discuss the following three species predator - pery system . we obtain existence , uniqueness and global asymptotic stability of almost periodic solution
在第四部分运用构造lyapunov函数的方法讨论了如下三种群食饵系统的概周期解的存在唯一性和全局渐近稳定性。 |
| 4. | The sufficient conditions ensuring existence and globally exponential stability of periodic solutions for neural networks with delays are obtained by using coincide degree , m - matrix theory and liapunov function method
摘要运用重合度理论、 m -矩阵理论及李雅普诺夫方法，获得了带时滞神经网络周期解存在性和全局指数稳定性的充分条件。 |
| 5. | 3 . we construct liapunov functions with separable variables and prove results on global stability with respect to partial variables for nonlinear and non - autonomous systems with separable variables
三、利用分离变量的liapunov函数，研究了非线性非自治分离变量系统关于部分变元的全局稳定性，将一般自治系统的相应结果推广到非自治系统。 |
| 6. | 2 . using techniques of liapunov functions and inner products , we extend the approach and the results in part i and give criterion on the stability , asymptotic stability and exponential stability with respect to partial variables for time - varying nonlinear systems
二、仍然使用上述方法再加上liapunov函数及内积等技巧，研究了非线性时变系统对部分变元的稳定性、渐近稳定性、指数稳定性，推广了第一部分结果。 |
