阻尼涨落对线性过阻尼分数阶振子共振的影响  

Effect of fluctuating damping on the resonant behavior of linear fractional over-damped oscillator

作　　者：林丽烽[1] 王会琦[2] 

机构地区：[1]福建农林大学计算机与信息学院,福州350002 [2]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2014年第6期1118-1124,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11301360);高等学校博士学科点专项科研基金(20120181120089);福建省教育厅科技项目(JA14112)

摘　　要：本文研究了具有涨落阻尼的线性过阻尼分数阶振子的共振现象.利用分数阶Shapiro-Loginov公式和Laplace变换,本文得到了系统响应的一阶稳态矩的解析表达式.对稳态响应的振幅增益的分析表明该系统存在三种不同形式的共振现象:bona fide共振、随机共振和广义随机共振,而分数阶的变化将导致bona fide共振的多样化.In this paper, the effect of fluctuating damping on the resonant behavior of linear fractional o- ver-damped oscillators is investigated. Using fractional Shapiro-Loginov formula and Laplace transform technique, an exact expression of the first-order moment of the system＇s steady response is obtained. Non-monotonic dependences of the steady response amplitude amplification on frequency of the periodic signal, noise parameters and fractional order indicate that the bona fide resonance, SR and SR in the wide sense coexist in this system. Specially, variety of the fractional order diversifies the bona fide reso- nance.

关 键 词：随机共振 分数阶振子 双态噪声 阻尼涨落 

分 类 号：O211.9[理学—概率论与数理统计]