Single and multiple vibrational resonance in a quintic oscillator with monostable potentials

Abstract

We analyze the occurrence of vibrational resonance in a damped quintic oscillator with three cases of single well of the potential V(x)=1/2omega(0)(2)x(2)+1/4betax(4)+1/6gammax(6) driven by both low-frequency force f cos omegat and high-frequency force g cos Omegat with Omega >> omega. We restrict our analysis to the parametric choices (i) omega(0)(2), beta, gamma > 0 (single well), (ii) omega(0)(2), gamma > 0, beta < 0, beta(2) < 4omega(0)(2)gamma (single well), and (iii) omega(0)(2) > 0, beta arbitrary, gamma < 0 (double-hump single well). From the approximate theoretical expression of response amplitude Q at the low-frequency omega we determine the values of omega and g (denoted as omega(VR) and g(VR)) at which vibrational resonance occurs. We show that for fixed values of the parameters of the system when omega is varied either resonance does not occur or it occurs only once. When the amplitude g is varied for the case of the potential with the parametric choice (i) at most one resonance occur while for the other two choices (ii) and (iii) multiple resonance occur. Further, g(VR) is found to be independent of the damping strength d while omega(VR) depends on d. The theoretical predictions are found to be in good agreement with the numerical result. We illustrate that the vibrational resonance can be characterized in terms of width of the orbit also.

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.…”

Enriched vibrational resonance in certain discrete systems

“…The occurrence of the VR phenomenon has been widely studied and reported by many researchers numerically [1][2][3] and experimentally [4][5][6][7][8]. Much studies have been carried out in a large class of dynamical systems such as monostable system [9], excitable system [10], bistable systems [1,11,12], time-delayed system [13] and also in a few lowdimensional maps [14] due to its importance in exhibiting the response of the system in an interesting way. An attempt to explore the phenomenon of vibrational resonance by Landa and McClintock [1] by replacing the background noise (stochastic resonance) with high-frequency signal in order to enhance the response of the system at the frequency of the driving force, has attracted much attention in recent years.…”

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].…”