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Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier

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  • Stan, Cristina
  • Cristescu, C.P.
  • Alexandroaei, D.
  • Agop, M.

Abstract

We report on stochastic resonance and vibrational resonance in an electric charge double layer configuration as usually found in electrical discharges, biological cell membranes, chemical systems and nanostructures. The experiment and numerical computation show the existence of a barrier expressible in terms of the golden mean above which the two phenomena do not take place. We consider this as new evidence for the importance of the golden mean criticality in the oscillatory dynamics, in agreement with El Naschie’s E-infinity theory. In our experiment, the dynamics of a charge double layer generated in the inter-anode space of a twin electrical discharge is investigated under noise–harmonic and harmonic–harmonic perturbations. In the first case, a Gaussian noise can enhance the response of the system to a weak injected periodic signal, a clear mark of stochastic resonance. In the second case, similar enhancement can appear if the noise is replaced by a harmonic perturbation with a frequency much higher than the frequency of the weak oscillation. The amplitude of the low frequency oscillation shows a maximum versus the amplitude of the high frequency perturbation demonstrating vibrational resonance. In order to model these dynamics, we derived an excitable system by modifying a biased van der Pol oscillator. The computational study considers the behaviour of this system under the same types of perturbation as in the experimental investigations and is found to give consistent results in both situations.

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  • Stan, Cristina & Cristescu, C.P. & Alexandroaei, D. & Agop, M., 2009. "Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 727-734.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:727-734
    DOI: 10.1016/j.chaos.2008.03.004
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    References listed on IDEAS

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    1. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    2. Stan, Cristina & Cristescu, C.P. & Agop, M., 2007. "Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1035-1040.
    3. Goldobin, D.S. & Pikovsky, A.S., 2005. "Synchronization of self-sustained oscillators by common white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(1), pages 126-132.
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    Cited by:

    1. Yao, Chenggui & Ma, Jun & He, Zhiwei & Qian, Yu & Liu, Liping, 2019. "Transmission and detection of biharmonic envelope signal in a feed-forward multilayer neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 797-806.
    2. Stan, Cristina & Cristescu, Cristina Maria & Alexandroaei, D. & Cristescu, C.P., 2014. "The effect of Gaussian white noise on the fractality of fluctuations in the plasma of a symmetrical discharge," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 46-55.
    3. Ge, Mengyan & Lu, Lulu & Xu, Ying & Mamatimin, Rozihajim & Pei, Qiming & Jia, Ya, 2020. "Vibrational mono-/bi-resonance and wave propagation in FitzHugh–Nagumo neural systems under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Liu, Shujun & Yang, Ting & Zhang, Xinzheng, 2015. "Effects of stochastic resonance for linear–quadratic detector," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 319-331.

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