物理学报Issue(7)：1-9,9.DOI:10.7498/aps.64.070507
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
摘要
Abstract
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 high-frequency 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 ofΩ≫ω(Ωis the frequency of the high-frequency signal and ω 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 Q can be obtained, and the effects of the time-delay parameterαand the asymmetric parameter r 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 Q-αplot, α can induce the Q 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 r. However, the resonance amplitude is enhanced with increasing r. Specifically, the resonance amplitude is greatly enhanced when r>0.15. On the other hand, in the symmetric case (r=0), BVR at which the vibrational resonance occurs is periodic with the periods of high-frequency signal and low-frequency signal as α increases, which is shown in BVR-α (B is the amplitude of the high-frequency signal) plot. In Q-Ωplot, Q is presented by multi-resonance at the small values of B andΩ, but Q tends to a fixed value at the small values of B and the large values ofΩ. We believe that the above theoretical observations will stimulate the experimental study of vibrational resonance in nonlinear oscillators and electronic circuits with time-delayed feedback.关键词
时滞/非对称双稳系统/振动共振Key words
time delay/asymmetric bistable system/vibrational resonance引用本文复制引用
杨秀妮,杨云峰..具有时滞反馈的非对称双稳系统中的振动共振研究[J].物理学报,2015,(7):1-9,9.基金项目
国家自然科学基金(批准号:71103143)和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 （批准号:71103143）
