具有时滞反馈的非对称双稳系统中的振动共振研究  

Vibrational resonance in an asymmetric bistable system with time-delay feedback

作　　者：杨秀妮[1] 杨云峰[1] 

机构地区：[1]西安科技大学理学院,西安710054

出　　处：《物理学报》2015年第7期152-159,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:71103143);陕西省科学技术研究发展计划项目(批准号:2013KJXX-40)资助的课题~~

摘　　要：研究了具有时滞反馈的非对称双稳系统中的振动共振现象.在绝热近似条件下,应用快慢变量分离法得到系统响应振幅的解析表达式,分析了时滞参数和不对称参数对振动共振现象的影响.结果表明:在-平台上,可以诱导响应幅值的极大值以输入高频信号和低频信号的周期出现.不对称参数并不影响共振发生的位置,但是能够增强响应幅值.在-(为高频信号振幅)平台上,共振发生的位置VR随着呈现两种不同的周期关系,且周期分别为输入高频信号和低频信号的周期.在-Ω(Ω高频信号频率)平台上,随着时滞参数的增大,当较小时,在Ω的小值区间内,呈现出多重共振现象,在Ω的大值区间,趋于定值.Vibrational resonance is a resonant dynamics induced by a high-frequency periodic force at the low-frequency of the input periodic signal, and the input periodic signal is enhanced by a high-frequency signal. In this paper, a linear time-delayed feedback bistable system with an asymmetric double-well potential driven by both low-frequency and highfrequency periodic forces is constructed. Based on this model, the vibrational resonance phenomenon is investigated.Making use of the method of separating slow motion from fast motion under the conditions of Ω（Ω is the frequency of the high-frequency signal and is the one of the low-frequency signal）, equivalent equations to the slow motion and the fast motion are obtained. Neglecting the nonlinear factors, the analytical expression of the response amplitude can be obtained, and the effects of the time-delay parameter and the asymmetric parameter on the vibrational resonance are discussed in detail. Moreover, the locations at which the vibrational resonance occurs, are obtained by means of solving the condition for a resonance to occur. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter, i.e. in-plot, can induce the which is periodic with the periods of the high-frequency signal and the low-frequency signal.The locations at which the vibrational resonance occurs are not changed by the asymmetric parameter. However,the resonance amplitude is enhanced with increasing. Specifically, the resonance amplitude is greatly enhanced when〉 0 15. On the other hand, in the symmetric case（= 0）, VR at which the vibrational resonance occurs is periodic with the periods of high-frequency signal and low-frequency signal as increases, which is shown in VR-（ is the amplitude of the high-frequency signal） plot. In Ω-Ω plot, is presented by multi-resonance at the small values of and Ω, but tends to a fixed value at the small values of and the la

关 键 词：时滞 非对称双稳系统 振动共振 

分 类 号：O321[理学—一般力学与力学基础]