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Numerical analyses of the vibrational resonance occurrence in a nonlinear dissipative system

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  • Usama, B.I.
  • Morfu, S.
  • Marquié, P.

Abstract

We carry out numerical analyses on a system which describes the motion of a particle experiencing periodic potential and submitted to both bichromatic input excitation and space-dependent nonlinear dissipative damping. The bichromatic driving models a low frequency signal corrupted by an additive high frequency perturbation which can enhance the detection of the low frequency stimulation via the Vibrational Resonance (VR) phenomenon. We focus on the combined effect of nonlinear dissipation and the mass of the particle on the occurrence of vibrational resonance. Depending on the mass of the particle, we demonstrate that the system exhibits two different behaviors, for one of which VR ceasing to exist. Furthermore, we propose an indicator which enable us to identify a critical value of mass below which VR phenomenon can be observed and beyond which no enhancement can be expected by perturbing the system with the high frequency component.

Suggested Citation

  • Usama, B.I. & Morfu, S. & Marquié, P., 2019. "Numerical analyses of the vibrational resonance occurrence in a nonlinear dissipative system," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 31-37.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:31-37
    DOI: 10.1016/j.chaos.2019.06.028
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    References listed on IDEAS

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    2. Bordet, M. & Morfu, S., 2013. "Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 82-89.
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    4. Duan, Fabing & Abbott, Derek, 2007. "Binary modulated signal detection in a bistable receiver with stochastic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 173-190.
    5. L. Gammaitoni & P. Hänggi & P. Jung & F. Marchesoni, 2009. "Stochastic Resonance: A remarkable idea that changed our perception of noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 1-3, May.
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    Cited by:

    1. Usama, B.I. & Morfu, S. & Marquie, P., 2021. "Vibrational resonance and ghost-vibrational resonance occurrence in Chua’s circuit models with specific nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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