Analytical Study of Vibrational Resonance in an Overdamped Bistable Oscillator

Chizhevsky, V. N.

doi:10.1142/s021812740802135x

Cited by 40 publications

(32 citation statements)

References 7 publications

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“…[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%

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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“…8 In the latter case, known as VR, the system is under the action of two frequency signal. [9][10][11] Such bichromatic signals are pervasive in many different fields, including brain dynamics, 12 where, for instance, bursting neurons may exhibit two widely different time scales.…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance in neuron populations

Deng¹,

Wang²,

Wei³

et al. 2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

122

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In this paper different topologies of populations of FitzHugh-Nagumo neurons have been introduce to investigate the effect of high-frequency driving on the response of neuron populations to a subthreshold low-frequency signal. We show that optimal amplitude of high-frequency driving enhances the response of neuron populations to a subthreshold low-frequency input and the optimal amplitude dependences on the connection among the neurons. By analyzing several kinds of topology (i.e., random and small world) different behaviors have been observed. Several topologies behave in an optimal way with respect to the range of low-frequency amplitude leading to an improvement in the stimulus response coherence, while others with respect to the maximum values of the performance index. However, the best results in terms of both the suitable amplitude of high-frequency driving and high stimulus response coherence have been obtained when the neurons have been connected in a small-world topology.

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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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Analytical Study of Vibrational Resonance in an Overdamped Bistable Oscillator

Cited by 40 publications

References 7 publications

Novel vibrational resonance in multistable systems

Novel vibrational resonance in multistable systems

Vibrational resonance in neuron populations

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

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