非线性常微分方程Lyapunov稳定性的导出在教学中的探究  

Exploration on the Teaching of Lyapunov Stability for Nonlinear Ordinary Differential Equation

作　　者：周伟松[1] 李小柳 

机构地区：[1]重庆邮电大学理学院,重庆400065 [2]广东省江门市鹤山市第一中学,广东鹤山529700

出　　处：《科教文汇》2017年第22期40-42,共3页Journal of Science and Education

基　　金：重庆市教委项目基金(KJ1704099);重庆邮电大学博士启动基金(A2016-80);重庆市信息与计算科学"三特"专业资助

摘　　要：1892年,苏联著名的数学力学家李雅普诺夫~[1](Lyapunov)给出的运动稳定性的严格数学定义具有划时代的意义,开创的判别稳定性的直接法(V函数法)已经成为常微分方程理论的重要分支。鉴于无需求出方程的解就可用来分析系统的稳定性这个极大的优越性,它受到众多科学家和学者的追捧~[2-4]。通过对Lyapunov稳定性以及V函数的构造的导出可以启发学生对常微分方程的理解和提高学习兴趣。In1892,the doctoral thesis entitled"The generalproblem of the stability of motion"by the former Soviet Union academicianLyapunov is first introduced.Its strict mathematicaldefinition of the Lyapunov stability is of epoch-making significance.Moreover,the Lyapunov direct method(V functionmethod)is an important branch of the theory of ordinary differentialequations.Since it can be used to analyze the stability of thesystem without solving the difficult differential equation,it hasbeen investigated by many scientists and scholars.Through theintroduction of Lyapunov stability and V function,it can stimulatestudents to understand the ordinary differential equation and inspiretheir interests.

关 键 词：LYAPUNOV稳定性 V函数 常微分方程 

分 类 号：G642[文化科学—高等教育学]