Novel vibrational resonance in multistable systems

Abstract

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.

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].…”

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] .…”

Vibrational resonance in a Hodgkin-Huxley neuron

“…Güvenilir olmayan sinaptik iletimin (unreliable synaptic transmission) ileri yönlü biyolojik nöron aglarında VR' ye etkileri Xue ve arkadaşları tarafından araştırılmıştır [20]. Bu çalışmaların yanı sıra uyarılabilir (excitability), tek-kararlı (monostable), iki-kararlı (bistable) ve çok-kararlı (multistable) davranışlar sergileyebilen Rulkov map ve Bellows map gibi ayrık zamanlı sistemlerde de VR etkisinin ortaya çıkabilecegi gösterilmiştir [21][22][23]. (1) Eşitligi ile ifade edilmektedir.…”