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微分方程的平衡点及稳定性分析

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对于微分方程平衡点稳定性的分析,有助于对混沌系统微分方程组的平衡点的判断。保山学院学报2010第2期接法需要求出系统的解析解,对于一些简单方程阵为:/(0-2|,p=4,g=4,故P00是系统的可能很容易求出,而对于一些复杂的方程(比如例稳定的平衡点2),我们是借助了数学软件求出的方程的通解;而在点21,0)处,系统的线性近似方程的系数矩直接法不用求方程的解就可以讨论平衡点的稳定性。我们在数学建模的过程中,有些系统不用求解阵为(0-2|,p=4,q=4,故P21,0是系统的方程,只需要研究平衡点的稳定状态所以用直接稳定的平衡点;法分析平衡点的稳定性是非常有用的。在点P处,系统的线性近似方程的系数矩10阵为A302|10=19=2,故P(2,是系统参考文:[冯杰,黄力伟等.数学建模原理与案例M北京科学的不稳定的平衡点;出版社,2007,1[2]张锦炎,冯贝叶.常微分方程几何理论与分支问题M3.结论北京:北京大学出版社,2005,8从上面的分析和例子可以看出,平衡点的稳3]阳明盛. Mathematic基础及数学软件M大连:大连理定性的讨论方法主要有间接法和直接法两种,间工大学出版社,2009Analyze of Differential Equation Balance Point StabilityWang Jingyan; Yang Yanli(Math Dept. Baoshan College, Baoshan, Yunnan, 678000)Abstract: This paper mainly discusses a step and the second-order differential equation balance pointhe stability, which plays the major role to its research of mathematics model stabilityKey words: autonomous system; balance point; stability微分方程的平衡点及稳定性分析旧WANFANG DATA文献链接作者:王景艳,杨艳丽, Wang Jingyan, Yang Yanl作者单位:保山学院,数学系,云南,保山,678000刊名:保山学院学报英文刊名:JOURNAL OF BAOSHAN TEACHERS COLLEGE年,卷(期):2010,29(2)参考文献(3条)1.阳明盛 Mathemat ica基础及数学软件20062.张锦炎;冯贝叶常微分方程几何理论与分支问题20053.冯杰;黄力伟数学建模原理与案例2007本文链接http://d.g.wanfangdata.comcn/periodiCalbsszxb201002014.aspx

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