Is the High-Frequency Signal Necessary for the Resonance in the Delayed System?

Abstract

In a delayed system excited by low-frequency and high-frequency signals, the necessity of the high-frequency signal on the resonance is discussed. By adjusting the delay time, the resonance occurs in a wide scope of frequencies, including the primary, subharmonic and superharmonic frequencies. Only for very few cases does the high-frequency signal have a positive effect on the resonance. It is the traditional vibrational resonance phenomenon. In most situations, the high-frequency excitation is unnecessary for the resonance. An appropriate delay, rather than the high-frequency signal, is the key factor in improving the weak low-frequency signal.

Bogdanov–Takens resonance in time-delayed systems

“…Equations like (1) may exhibit something extremely similar [18,28]. The autonomous systeṁ x+x((1+α)x 2 −1)−αx τ = 0 shows slowly damped oscillations around +1 or −1, induced by the delay.…”

Delay-induced resonance suppresses damping-induced unpredictability

“…In particular, vibrational resonance (VR) [13,14] is a well-known resonance phenomenon in which the amplitude enhancement is triggered by two periodic external forcings with different frequencies. The delay term can play the role of one of the periodic forcings typically used in vibrational resonance, and the resonance can be triggered by the cooperation of the time delay and just one external periodic forcing as shown in [15]. The latter phenomenon has been called delay-induced resonance and has been studied among other fields in the context of meteorology, as for example the ENSO model in [16].…”

Delay-Induced Resonance in the Time-Delayed Duffing Oscillator

“…We mention here some of these cases. The question of the need of a high-frequency forcing when a time-delay is present was already posed by LV et al [ 2015]. The effect of the time-delay in the periodically driven damped Duffing oscillator was analyzed in [Ravichandran et al, 2012] using a perturbation theory.…”