常微分方程=Q(x,y),=P(x)全局渐近稳定性的条件  

The Condition for the Global Stability of the System x·=Q(x,y),y·=P(x)

作　　者：黄世中[1] 权宏顺[1] 

机构地区：[1]兰州大学数学系

出　　处：《兰州大学学报（自然科学版）》1999年第1期25-29,共5页Journal of Lanzhou University(Natural Sciences)

摘　　要：在常微分方程的定性理论中，研究一个系统的全局渐近稳定性是一项困难且有意义的课题，通常采用构造Ｌｉａｐｕｎｏｖ函数并利用稳定性理论中的有关定理来解这一难题．本文利用Ｄｕｌａｃ函数法，首先判定了不存在绕平衡点的闭轨线，然后利用Ｆｉｌｉｐｐｏｖ变换和比较定理，证明了系统所有轨线的有界性，进而得到了平衡点是全局渐近稳定的．所研究的方程比前人研究的更一般。In the qualitative theory of ODE, the study of global stability of a certain system is a difficult but significant subject. Usually, the construction of the Liapunov function and some related theorems of stable theory of ODE are used in the problem. In this paper, the nonexistence of the closed orbit which circles the equilibrium is proved by using the Dulac function, then all the orbits of the system are bounded by the Filippov transformation and comparability theorem. The system studied in this paper is more general than those studied formerly and the way of studying is innovative. The two criterions developed are new and useful.

关 键 词：有界性 全局稳定性 常微分方程 渐近稳定性 

分 类 号：O175.13[理学—数学]