一类非线性时滞系统的定性分析  

QUALITATIVE ANALYSIS FOR A CLASS OF NONLINEAR DELAY SYSTEM

作　　者：赵杰民[1] 

机构地区：[1]中国金融学院,北京100029

出　　处：《数学杂志》2000年第4期403-409,共7页Journal of Mathematics

基　　金：中国金融学院科研基金资助项目!( 1 999)

摘　　要：本文通过 Liapunov泛函方法和应用 Razumikhin定理获得了一类非线性时滞系统的若干定理 ,并推广了一些已知的结论 .应用获得的定理还解决了实际问题 .In this paper,the second order nonlinear delay system(t)=y(t), (t)=h(y(t))∫ o -τ K(x(t+s))y(t+s) d s-f(y(t))-h(y(t))g(x(t))+p(t) is considered. We obtain some theorems on stability, boundedness, existence of periodic motions and stationary oscillation by means of the method of Liapunov functional and Razumikhin type theorem. A concise expression about the accurate bounds of delay are obtained. Some theorems in this paper include some well known results as their special cases. Finally, the theorems are applied to a feedback system with a restoring force which was introduced by Prof. T. A. Burton, and some useful results are obtained.

关 键 词：LIAPUNOV泛函 平稳振荡 非线性时滞系统 定性分析 

分 类 号：O175.12[理学—数学]