Vibrational resonance and the detection of aperiodic binary signals

Chizhevsky, V. N.; Giacomelli, Giovanni

doi:10.1103/physreve.77.051126

Cited by 73 publications

(30 citation statements)

References 28 publications

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“…6,8,9 The occurrence of VR has been studied in a monostable, 10 bistable, 1,8,9,11,12 and three well 13 systems. Moreover, it has been also analyzed in excitable systems, 14 vertical cavity surface emitting laser, 15,16 coupled oscillators, 4,17,18 and time-delay systems. [19][20][21][22] Very recently, VR is found to induce undamped low-frequency signal propagation in one-way coupled 17 and globally coupled 23 bistable systems.…”

Section: Introductionmentioning

confidence: 99%

Novel vibrational resonance in multistable systems

Rajasekar

Abirami²,

Sanjuán³

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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.

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Section: Introductionmentioning

confidence: 99%

Novel vibrational resonance in multistable systems

Rajasekar

Abirami²,

Sanjuán³

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…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.…”

Section: Introductionmentioning

confidence: 98%

Enriched vibrational resonance in certain discrete systems

Jeevarekha¹,

Santhiah²,

Philominathan³

2014

Pramana - J Phys

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We wish to report the occurrence of vibrational resonance in certain discrete systems like sine square map and sine circle map, in a unique fashion, comprising of multiple resonant peaks which pave the way for enrichment. As the systems of our choice are capable of exhibiting vibrational resonance behaviour unlike the earlier reports, they are taken for investigation and the necessary numerical and analytical results are presented. Further, we study the effect of external forcing on various attractors of these systems with appropriate bifurcation and Lyapunov exponent diagrams.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Venkatesh

Venkatesan

2016

Pramana - J Phys

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Additional sinusoidal and different non-sinusoidal periodic perturbations applied to the periodically forced nonlinear oscillators decide the maintainance or inhibitance of chaos. It is observed that the weak amplitude of the sinusoidal force without phase is sufficient to inhibit chaos rather than the other non-sinusoidal forces and sinusoidal force with phase. Apart from sinusoidal force without phase, i.e., from various non-sinusoidal forces and sinusoidal force with phase, square force seems to be an effective weak perturbation to suppress chaos. The effectiveness of weak perturbation for suppressing chaos is understood with the total power average of the external forces applied to the system. In any chaotic system, the total power average of the external forces is constant and is different for different nonlinear systems. This total power average decides the nature of the force to suppress chaos in the sense of weak perturbation. This has been a universal phenomenon for all the chaotic non-autonomous systems. The results are confirmed by Melnikov method and numerical analysis. With the help of the total power average technique, one can say whether the chaos in that nonlinear system is to be supppressed or not.

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Vibrational resonance and the detection of aperiodic binary signals

Cited by 73 publications

References 28 publications

Novel vibrational resonance in multistable systems

Novel vibrational resonance in multistable systems

Enriched vibrational resonance in certain discrete systems

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

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