Vibrational Resonance in an Asymmetric Duffing Oscillator

Abstract

We analyze how the asymmetry of the potential well of the Duffing oscillator affects the vibrational resonance. We obtain, numerically and theoretically, the values of the low-frequency and amplitude of the high-frequency forces at which vibrational resonance occurs. Furthermore, we observe that an additional resonance is induced by the asymmetry of the potential well. We account the additional resonance in terms of resonant frequency of the slow motion of the system. Resonance occurs in the asymmetric system for the input signal frequency range for which it is not possible in the symmetric system. Resonance is also studied with nonsinusoidal input signals and in the presence of additive Gaussian white noise.

Vibrational resonance in the Morse oscillator

“…In this connection we point out that (i) one or more resonances in monostable systems [11], (ii) a sequence of resonance peaks in a spatially periodic potential system [12], (iii) additional resonances due to asymmetry in the potential [25], periodic and quasiperiodic occurrence of resonance peaks in time-delayed feedback systems [26][27][28][29] and large amplitude of vibrational resonance at the dynamic bifurcation point [30] have been reported.…”

Vibrational resonance in a harmonically trapped potential system

“…It is important to investigate the role of shape of potentials on vibrational resonance. In this direction, the occurrence of vibrational resonance has been examined in bistable [16][17][18][21][22][23][24] , monostable [25] , asymmetric [26] , spatially periodic [27] and spatially extended single-well [28] potentials systems. It has also been analyzed in an excitable system [29] and in a system with signum nonlinearity [30] .…”

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

“…Such a resonant behaviour is known as vibrational resonance [43][44][45]. These phenomena have been realized in various theoretical models [39,[46][47][48][49][50][51][52][53][54][55][56][57][58][59] and experimental systems [60][61][62][63][64][65][66].…”