周期变系数常微分方程动力系统稳定性分析的Liapunov指数判据  

A Criterion of Dynamic Stability on Ordinary Differential Equations with Periodically Variable Coefficients by Liapunov Characteristic Number

作　　者：郑晓静[1] 武建军[1] 周又和[1] 

机构地区：[1]兰州大学力学系

出　　处：《兰州大学学报（自然科学版）》1999年第2期17-20,共4页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金;国家杰出青年科学基金;国家教委高校博士点专项基金;国防科工委科研项目;西安交通大学机械结构强度与振动国家重点实验室基金

摘　　要：对于周期变系数常微分方程（组）描述的动力系统，建立了稳定性分析的Ｌｉａｐｕｎｏｖ指数的判别准则：当其动力系统的全部Ｌｉａｐｕｎｏｖ特征指数小于零时，动力系统就是稳定性的；否则，如果动力系统中只要有一个Ｌｉａｐｕｎｏｖ特征指数大于零，则动力系统就丧失稳定性．这一判别方法对于高维变系数常微分方程动力系统，相对于稳定性分析的Ｆｌｏｑｕｅｔ经典方法而言。A criterion of dynamic stability for a set of ordinary differential equations with periodically variable coefficients by means of the Liapunov characteristic number is given. The obtained criterion is that when all of the Liapunov characteristic numbers of the system are less than zero, the dynamic system is stable; otherwise, if one Liapunov characteristic number is greater than zero in the system, the dynamic system becomes unstable. This criterion has the merits of smaller computation and simpler searching method as compared with the method based on the Floquet theory which needs to search all characteristic values of matrix of basic solutions of the dynamic system when the system is of high dimension.

关 键 词：周期变系数 常微分方程 动力系统 稳定性 

分 类 号：O175.13[理学—数学]