Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise
Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise
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DOI：
10.1016/j.chaos.2015.05.029
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发表时间：
2015-08
影响因子：
7.8
通讯作者：
Yong-Ge Yang;Wei Xu;X. Gu;Yahui Sun
中科院分区：
文献类型：
--
作者：
Yong-Ge Yang;Wei Xu;X. Gu;Yahui Sun
研究了一类具有Caputo型分数阶导数的自激系统在高斯白色噪声驱动下的随机响应。首先，将广义调和函数方法应用于分数阶自激系统。基于该方法，将原分数阶自激系统化为不含分数阶导数的等价随机系统。然后，利用随机平均法得到了等效随机系统的解析解。最后，为了验证理论结果，详细讨论了两个最典型的分数阶导数自激系统，即分数阶货车der Pol振子和分数阶Rayleigh振子。同时，还详细讨论了分数阶数、分数阶系数和高斯白色噪声强度对自激分数阶系统的影响。
The stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise is considered. Firstly, the generalized harmonic function technique is applied to the fractional self-excited systems. Based on this approach, the original fractional self-excited systems are reduced to equivalent stochastic systems without fractional derivative. Then, the analytical solutions of the equivalent stochastic systems are obtained by using the stochastic averaging method. Finally, in order to verify the theoretical results, the two most typical self-excited systems with fractional derivative, namely the fractional van der Pol oscillator and fractional Rayleigh oscillator, are discussed in detail. Comparing the analytical and numerical results, a very satisfactory agreement can be found. Meanwhile, the effects of the fractional order, the fractional coefficient, and the intensity of Gaussian white noise on the self-excited fractional systems are also discussed in detail.