| 有限时滞Lienard方程Hopf分支的数值逼近 |
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| 引用本文： | 李春萍,王宏艳,王洪梅.有限时滞Lienard方程Hopf分支的数值逼近[J].石家庄学院学报,2007,9(6):22-25. |
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| 作者姓名： | 李春萍 王宏艳 王洪梅 |
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| 作者单位： | 1. 河北金融学院,基础部,河北,保定,071009
2. 华北电力大学,基础部,河北,保定,071000 |
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| 摘 要： | 研究了一类有限时滞的Lienard方程Hopf分支的数值逼近问题．首先，以滞量为参数，应用Cooke和JHale的方法，得到Hopf分支存在的条件；然后，利用欧拉方法将得到的差分方程表示为映射，利用离散动力系统的分支理论，给出了差分方程Hopf分支存在的奈件和连续系统与其数值逼近间的关系．证明了当该系统在r=ro产生Hopf分支时，其数值逼近也在相应的参数rh处具有Hopf分支，并且忙rb=ro＋o（h）．
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| 关 键 词： | Lienard方程 欧拉方法 Hopf分支 数值逼近 |
| 文章编号： | 1673-1972（2007）06-0022-04 |
| 修稿时间： | 2007-04-19 |
Hopf Bifurcation in Numerical Approximation for a Lienard Equation with Finite Delay |
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| LI Chun-ping,WANG Hong-yan,WANG Hong-mei.Hopf Bifurcation in Numerical Approximation for a Lienard Equation with Finite Delay[J].Journal of Shijiazhuang University,2007,9(6):22-25. |
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| Authors: | LI Chun-ping WANG Hong-yan WANG Hong-mei |
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| Institution: | 1.DePartment of Basic Courses, Hebei Financial College, Baoding, Hebei 071009, China ; 2.Department of Basic Courses, North China University of Electric Power, Baoding, Hebei 071000, China |
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| Abstract: | The numerical approximation of a Lienard equotion with finite delay is discussed. Firstly, regarding the delay as a parameter and employing the method of Cooke and J. Hale ,the conditions to the existence of Hopf bifurcation at some valus of the delay are given. Then ,the dalay deference equation obtained by using Euler method is written as a map. According to the theories of bifurcation for discrete dynamical systems,the conditions to the existence of Hopf bifurcation for numerical approximation are given. The relations of Hopf bifurcation between the continuous and the discrete are discussed. That when this model has Hopf bifurcation ,the numerical approximation also has Hopf bifurcation is proved. |
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| Keywords: | Lienard equotion Euler method Hopf bifurcation numerical approximation |
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