Analysis of vibrational resonance in a quintic oscillator

Jeyakumari, S.; Chinnathambi, V.; Rajasekar, S.; Sanjuán, Miguel A. F.

doi:10.1063/1.3272207

Cited by 75 publications

(48 citation statements)

References 29 publications

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“…0 for sufficiently large values of g because of the monotonic increase of the resonant frequency for large values of g. 1,8,10,12,13 In the pendulum system, since x 2 r ¼ J 0 j j ! 0 as g !…”

Section: Underdamped Pendulum Systemmentioning

confidence: 98%

“…[2][3][4][5][6][7] Theoretical approaches have been developed to study VR. 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.…”

Section: Introductionmentioning

confidence: 99%

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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: Underdamped Pendulum Systemmentioning

confidence: 98%

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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“…This method has been used in the theoretical analysis of the Duffing oscillator [Gitterman, 2001;Blekhman & Landa, 2004], the quintic oscillator [Jeyakumari et al, 2009a;Jeyakumari et al, 2009b], the delayed system [Jeevarathinam, 2011], the friction system [Thomsen, 1999], the supported beam [Tcherniak, 1999], the ratchet system [Borromeo & Marchesoni, 2006], the fractional-order system [Yang & Zhu, 2012, etc. among others.…”

Section: Theoretical Analysismentioning

confidence: 99%

Saddle-Node Bifurcation and Vibrational Resonance in a Fractional System with an Asymmetric Bistable Potential

Yang

Sanjuán

Tian

et al. 2015

Int. J. Bifurcation Chaos

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We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend on the potential well where the motion takes place. And consequently for numerical simulations, the initial condition is a key and important factor. To overcome this technical problem, a method is proposed to calculate the bifurcation and response amplitude numerically. The numerical results are in good agreement with the analytical predictions, indicating the validity of the numerical and theoretical analysis. The results show that the fractional-order of the fractional system induces one saddle-node bifurcation, while the asymmetric parameter associated to the asymmetric nature of the potential function induces two saddle-node bifurcations. When the asymmetric parameter vanishes, the saddle-node bifurcation turns into a pitchfork bifurcation. There are three kinds of vibrational resonance existing in the system. The first one is induced by the high-frequency signal. The second one is induced by the fractional-order. The third one is induced by the asymmetric parameter. We believe that the method and the results shown in this paper might be helpful for the analysis of the response problem of nonlinear dynamical systems.

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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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Analysis of vibrational resonance in a quintic oscillator

Cited by 75 publications

References 29 publications

Novel vibrational resonance in multistable systems

Novel vibrational resonance in multistable systems

Saddle-Node Bifurcation and Vibrational Resonance in a Fractional System with an Asymmetric Bistable Potential

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

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