| 强Van der Pol振子的谐波与修正算法 |
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| 引用本文： | 国忠金,梁以德,马晓燕.强Van der Pol振子的谐波与修正算法[J].大学物理,2009,28(3). |
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| 作者姓名： | 国忠金 梁以德 马晓燕 |
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| 作者单位： | 1. 泰山学院,数学与系统科学系,山东,泰安,271021
2. 香港城市大学,建筑工程系,香港,九龙 |
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| 摘 要： | 引入谐波平衡近似解的符号运算与同伦延拓法,获得了强Van der Pol振子的解析近似极限环与稳定响应.为提高其近似精度,给出了谐波解的修正算法,并与数值模拟比较.结果表明,该算法非常精确可靠,是研究强非线性动力学系统的有效分析方法.
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| 关 键 词： | 谐波平衡 同伦延拓法 修正算法 极限环 |
Harmonic wave and correction algorithm for forced Van der Pol oscillator |
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| GUO Zhong-jin,Andrew.Y.T.Leung,MA Xiao-yan.Harmonic wave and correction algorithm for forced Van der Pol oscillator[J].College Physics,2009,28(3). |
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| Authors: | GUO Zhong-jin AndrewYTLeung MA Xiao-yan |
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| Institution: | 1.Department of Mathematics and Systerns Science;University of Taishan;Taian Shandong 271021;China;2.Building and Construction;City University of Hong Kong;Hong Kong;China |
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| Abstract: | The sign algorithm of the harmonic balance approximate solutions and homotopy continuation method are introduced to get the analytic limit cycle and steady state response of the forced Van der Pol oscillator.In order to enhance precision,a correction algorithm is proposed.The approximate solution presented here is compared with numerical simulation.It is shown that the algorithm is very accurate,reliable and also an effective way of analyzing strong nonlinear systems. |
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| Keywords: | harmonic balance homotopy continuation method correction algorithm limit cycle |
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