Matlab在判断平面自治系统零解稳定性中的应用  

APPLICATION OF MATLAB IN JUDGING STABILITY OF ZERO SOLUTION FOR PLANAR AUTONOMOUS SYSTEMS

作　　者：李涧萍 范进军 Li Jianping;Fan Jinjun(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《山东师范大学学报（自然科学版）》2021年第2期132-137,共6页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11971275);山东省自然科学基金资助项目(ZR2019MA048).

摘　　要：旨在研究一类难以找到合适的Lyapunov函数的自治系统的零解稳定性问题.从零解稳定性的几何特征出发,基于零解稳定性理论,通过Matlab编程,结合平面自治系统的具体实例,在相平面上绘制出相应系统在原点附近的线素场,观察其走向,以此来分析零解的稳定性.然后,再利用Lyapunov第二方法,从理论上对得到的结论加以证明.本文从定性的角度探究自治系统零解的稳定性问题,不仅揭示了零解稳定性的本质特征,而且提供了更为便捷、直观的方法来判断微分方程零解的稳定性.This paper aims to judge the stability of zero-solution of differential equations for a class of planar autonomous systems where they are difficult to find Lyapunov functions.Based on the stability theory and geometric properties of the stability of zero-solution in differential equations,Matlab programming are introduced.Combined with specific examples,the line prime field of the corresponding system near the origin is plotted on the phase plane to analyze the stability of zero-solution.Finally,Lyapunov′s second method is used to prove the above conclusion theoretically.This paper explores the stability of zero-solution of differential equations from a qualitative point of view,which not only reveals the essential characteristics of the stability of zero-solution,but also provides a more convenient and intuitive way to judge the stability of zero-solution of differential equations.

关 键 词：平面自治系统 零解 稳定性 MATLAB 编程 

分 类 号：O17[理学—数学]