The Influence Of System Parameters And Time Delay On The Vibration Resonance Of The Three-stable System

Under both low-frequency and high-frequency signals,the response to a weak low-frequency signal can be maximized by modulating the high-frequency signal in a nonlinear system,this phenomenon is called vibrational resonance.The bi-harmonic signals mentioned here are ubiquitous in nature and cut across different fields,including brain dynamics,laser physics,acoustics,communication technology,neuroscience,etc.Therefore,it is necessary to study vibrational resonance.By the combination of theoretical analysis and numerical simulation,the effect of potential function parameters and the time delay on vibrational resonance is investigated in a quintic oscillator.Firstly,the impact of depth of the wells and the distance between the neigh-boring wells are systematically discussed in a quintic oscillator which has triple-well potential.It is found that:as ? varies,at most one resonance takes place and the response amplitude at resonance depends on the depth and the location of the poten-tial wells.When g is altered,the depth and location of wells can control the number of resonances,resulting in the observation of two,three and four resonances.Based on this,a method that can adjust the system parameters to achieve the optimum vibrational resonance by controlling the depth or the distance of wells is proposed,this method reduces the number of tunable parameters in the system.Secondly,the influence of linear time delay on vibrational resonance is con-sidered in quintic oscillator with triple-well potential driven by both low-frequency and high-frequency periodic forces.This task is performed through both theoretical approach and numerical simulation.It is found that:the time delay intensity will cause the number of resonances to change,and the greater time delay intensity,the smaller response amplitude at low frequency.On the other hand,with the change of delay time,the vibrational resonance phenomenon has two different periods at the same time,which is exactly equal to the period of the input high-frequency signal and low-frequency signal respectively.Furthermore,theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation.