Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Jeevarathinam, C.; Rajasekar, S.; Sanjuán, Miguel A. F.

doi:10.1103/physreve.83.066205

Cited by 102 publications

(48 citation statements)

References 42 publications

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“…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. Vibrational ratchet motion is studied in certain systems with spatially periodic potentials driven by a biharmonic force and a Gaussian white noise.…”

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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“…To implement the method of direct separation of time scale [48][49][50][51][52], we separate the variable x into a slow part X and a fast part ψ…”

Section: Direct Separation Of Time Scalesmentioning

confidence: 99%

Profiling the overdamped dynamics of a nonadiabatic system

et al. 2015

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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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Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Cited by 102 publications

References 42 publications

Novel vibrational resonance in multistable systems

Novel vibrational resonance in multistable systems

Profiling the overdamped dynamics of a nonadiabatic system

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

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