Residue harmonic balance method for generalized fractional order Van der Pol oscillator

机译：广义分数阶范德波尔振荡器的残余谐波平衡方法

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In this paper, a generalized fractional order Van der Pol (fVDP) oscillator is introduced. The residue harmonic balance method is used for generating the higher-order approximations to the angular frequency and period solution of generalized fVDP oscillator. This method combines the features of homotopy and harmonic balance to obtain approximate solutions to any desired accuracy. The zeroth order approximation is achieved using just one Fourier term. To improve the accuracy of approximate solutions, the unbalanced residues appearing in the harmonic balance equations are iteratively considered by introducing an order parameter to keep track of the approximation order. The results reveal that the proposed method is very effective and simple for obtaining asymptotic solutions of nonlinear oscillation systems containing fractional derivatives.

机译：本文介绍了广义分数阶范德波尔（fVDP）振荡器。残余谐波平衡法用于生成广义fVDP振荡器角频率和周期解的高阶近似。该方法结合了同伦和谐波平衡的功能，以获得任何所需精度的近似解。零阶近似仅使用一个傅立叶项即可实现。为了提高近似解的精度，通过引入阶次参数以跟踪近似阶次，来迭代考虑谐波平衡方程中出现的不平衡残差。结果表明，该方法对于求解包含分数阶导数的非线性振动系统的渐近解是非常有效和简单的。

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来源
《Proceedings of the Fifth symposium on fractional differentiation and its applications》|2012年|1-7|共7页
会议地点 Nanjing(CN)
作者
A.Y.T. Leung; H.X. Yang; Z.J. Guo;
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作者单位

Department of Civil and Architectural Engineering, City University of Hong Kong;

Department of Civil and Architectural Engineering, City University of Hong Kong;

Department of Civil and Architectural Engineering, City University of Hong Kong;

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会议组织
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Residue harmonic balance method; Generalized fractional Van der Pol oscillator; Analytical approximation; Limit cycle.;

机译：残余谐波平衡法;广义分数范德波尔振荡器;解析逼近;极限周期;

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Residue harmonic balance method for generalized fractional order Van der Pol oscillator

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