Experimental evidence, numerics, and theory of vibrational resonance in bistable systems

Baltanás, J. P.; López, Luis; Blechman, I. I.; Landa, P. S.; Zaikin, Alexey; Kurths, Jürgen; Sanjuán, Miguel A. F.

doi:10.1103/physreve.67.066119

Cited by 174 publications

(125 citation statements)

References 28 publications

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“…After this seminal work VR has been studied in a bistable oscillator [7], a Duffing oscillator [8], excitable systems [9] and spatially extended systems [10]. Experimental evidences of VR in a vertical cavity surface emitting laser [11], simple electronic circuit [9] and in an overdamped Duffing oscillator [12] have been reported.…”

Section: Introductionmentioning

confidence: 99%

Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators

Gandhimathi

Rajasekar

Kurths³

2006

Physics Letters A

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We study the overdamped version of two coupled anharmonic oscillators under the influence of both low-and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented.

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Section: Introductionmentioning

confidence: 99%

Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators

Gandhimathi

Rajasekar

Kurths³

2006

Physics Letters A

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“…With this work, we have attempted to provide a theoretical complement to the numerical study of the influence of additive noise on VR carried out in Ref. [17].…”

Section: Discussionmentioning

confidence: 99%

“…On the one hand, the fraction corresponding to the high-frequency region advances the appearance of the maximum. On the other hand, the remaining contribution masks the high-frequency force, decreasing its relative importance [17]. To shed some more light on this question, an extension of the theoretical approach put forward in Ref.…”

Section: Description Of the Model And Characterization Of Vrmentioning

confidence: 99%

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Effects of additive noise on vibrational resonance in a bistable system

Casado‐Pascual

Baltanás

2004

Phys. Rev. E

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We study the overdamped motion of a particle in a bistable potential subject to the action of a bichromatic force and additive noise, within the context of the vibrational resonance phenomenon. Under appropriate conditions, we obtain analytical expressions for the relevant observables which quantifies this phenomenon. The theoretical results are compared with those obtained by the numerical solution of the stochastic differential equation which describes the dynamics of the system. The limits of validity of the theoretical approach are also discussed.

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“…The occurrence of vibrational resonance has been analyzed in systems with monostable [11], bistable [3][4][5], spatially periodic states [12], excitable systems [13,14], coupled oscillators [15] and small world networks [14,16,17]. Experimental evidence of vibrational resonance in vertical cavity laser system [18][19][20] and in an electronic circuit [21] has also been reported.…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance in the Morse oscillator

2013

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We investigate the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies ω and Ω with Ω ≫ ω. In the damped and biharmonically driven classical Morse oscillator applying a theoretical approach we obtain an analytical expression for the response amplitude at the low-frequency ω. We identify the conditions on the parameters for the occurrence of the resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/(dω) where d is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. We have observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. We also report the occurrence of resonance and anti-resonance of transition probability of quantum mechanical Morse oscillator in the presence of the biharmonic external field. 46.40.Ff.

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Experimental evidence, numerics, and theory of vibrational resonance in bistable systems

Cited by 174 publications

References 28 publications

Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators

Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators

Effects of additive noise on vibrational resonance in a bistable system

Vibrational resonance in the Morse oscillator

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