Oscillatory region and asymptotic solution of fractional van der Pol oscillator via residue harmonic balance technique
Oscillatory region and asymptotic solution of fractional van der Pol oscillator via residue harmonic balance technique
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DOI：
10.1016/j.apm.2011.02.007
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发表时间：
2011-08
影响因子：
5
通讯作者：
Zhongjin Guo;A. Leung;H. X. Yang
中科院分区：
文献类型：
--
作者：
Zhongjin Guo;A. Leung;H. X. Yang
基于谐波平衡法，提出了一种预测和生成分数阶微分系统稳态解的强有力的分析方法。零阶近似，仅使用一个傅立叶项被施加到预测的分数货车der Pol振荡器的振荡和非振荡区域之间的边界的参数函数。通过求解线性代数方程组来迭代考虑傅立叶截断引起的不平衡留数，从而不断提高解的精度。得到了分数阶货车der Pol振子的角频率和极限环的高精度解，并进行了比较。结果表明，本文所述的方法是非常有效的，简单的获得渐近解的分数阶导数的非线性系统。
In this paper, a powerfully analytical technique is proposed for predicting and generating the steady state solution of the fractional differential system based on the method of harmonic balance. The zeroth-order approximation using just one Fourier term is applied to predict the parametric function for the boundary between oscillatory and non-oscillatory regions of the fractional van der Pol oscillator. The unbalanced residues due to Fourier truncation are considered iteratively by solving linear algebraic equations to improve the accuracy of the solutions successively. The highly accurate solutions to the angular frequency and limit cycle of fractional van der Pol oscillator are obtained and compared. The results reveal that the technique described in this paper is very effective and simple for obtaining asymptotic solution of nonlinear system having fractional order derivative.