The Effect Of Time Delay On Vibration Resonance In Nonlinear Systems

The analysis of dynamic chaxacteristics caused by two different frequency sig-nals has attracted a lot of scholars' attention in the fields of communication tech-nology,acoustics,neuroscience,laser physics,etc.This feature mainly reflects the phenomenon that the response amplitude of the system at the low-frequency can be amplified excellently by adjusting the relatively high-frequency input signal.This meaningful phenomenon is called vibrational resonance.The information of the sys?tem is usually carried by low frequency signals,so studying vibrational resonance has profound significance.In this paper,the harmonically trapped potential system and the period po?tential system are taken as the research objects,the amplitude of the response amplitude at the low frequency of the system is used as an indicator to measure the vibration resonance behavior.The theoretical analytical expression of the response amplitude of the system at low-frequency is obtained by means of the direct sepa-ration of the slow and fast motions.We focus on the effocts of time delay parameter and time delay term intensity parameter on the response amplitude of the system at low-frequency,and obtain some effective ways to control the vibration resonance behavior.The main contents and conclusions of this paper are as follows:We discuss the effects of time delay parameter on the vibrational resonance behavior of two systems.Firstly,with time delay parameter r changing,the response amplitude shows a periodic behavior,and the resonance phenomenon appears at some special values of ?.This means the value of Q can be amplified by adjusting?.Secondly,when the high frequency amplitude F takes different,values,which have different amplification on the response amplitude of the system with the same ?.This reveals that via the cooperation of F and r,the response amplitude of the system can also be magnified.Thirdly,with the variation of time delay parameter?,Q is a periodic function with 2?/? no matter how F changes.Which is exactly equal to the period of the input low-frequency signal.when the the strength of time delay parameter r was regarded as the constant,the two system with time delay shows a stronger resonance than that of without time delay even if F in the same intervals.By adjusting the time delay strength parameter r,the response amplitude can be increased,more importantly,the amplitude of response obtained by adjusting ? is much larger than that by adjusting ?.What's more,the weak low-frequency signal can be amplified by the synergy between the parameters ? and ?.This reminds us of an optimal way to magnify the weak low-frequency signal.We hope our conclusions will play a potential value in the field of signal processing.