A homotopy analysis method for limit cycle of the van der Pol oscillator with delayed amplitude limiting

被引：12
作者：
Eigoli, Ali Kamali [1 ]
Khodabakhsh, Mohammad [2 ]
机构：
[1] Islamic Azad Univ, Takestan Branch, Dept Mech Engn, Takestan, Iran
[2] Sharif Univ Technol, Dept Mech Engn, Tehran 113659567, Iran
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 22期
关键词：
van der Pol oscillator; Delayed amplitude limiting; Limit cycle; Homotopy analysis method; EQUATIONS;
D O I：
10.1016/j.amc.2011.04.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, a powerful analytical method, called Liao's homotopy analysis method is used to study the limit cycle of a two-dimensional nonlinear dynamical system, namely the van der Pol oscillator with delayed amplitude limiting. It is shown that the solutions are valid for a wide range of variation of the system parameters. Comparison of the obtained solutions with those achieved by numerical solutions and by other perturbation techniques shows that the utilized method is effective and convenient to solve this type of problems with the desired order of approximation. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：9404 / 9411
页数：8
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