摘要
本文研究了加性脉冲噪声驱动的线性分数阶调和振子的扩散行为.利用Laplace变换、双Laplace变换技巧及脉冲微分方程的基本性质,本文得到了振子位移的均值、方差、关联函数及均方位移.这些量均可以通过三参数的广义Mittag-Leffler函数来表示.然后,基于Mittag-Leffler函数的渐进性质,本文研究了振子的短时和长时扩散行为.研究表明,加性脉冲噪声增强振子的短时超扩散,并抬升振子的长时欠扩散均方位移.
Diffusion of a linear fractional impulsive noise is investigated. By using basic properties of impulsive differential harmonic oscillator driven by both thermal noise and additive the Laplace and double Laplace equation, the mean, variance, transform techniques and some correlation function and mean square displacement （MSD） of the oscillator are expressed by generalized Mittag-Leffler functions with three parameters. Furthermore, asymptotic diffusion of the oscillator is investigated in terms of the asymptotic properties of generalized Mittag-Leffler function. It is shown that the additive impulsive noise enhances the ballistic diffusion of the oscillator for short time-lag and adds a constant to the MSD for long time-lag.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2017年第5期929-934,共6页
Journal of Sichuan University(Natural Science Edition)
基金
桥梁无损检测与工程计算四川省高校重点实验室开放基金(2015QYJ06)
关键词
分数阶调和振子
均方位移
脉冲噪声
扩散
Fractional harmonic oscillator
Mean square displacement
Impulsive noise： Diffusion
