IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i2p727-734.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908001392
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.03.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cristescu, C.P. & Mereu, B. & Stan, Cristina & Agop, M., 2009. "Feigenbaum scenario in the dynamics of a metal–oxide semiconductor heterostructure under harmonic perturbation. Golden mean criticality," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 975-980.
    2. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    3. Yuan, De-you & Du, Shu-de & Cheng, Zheng-xing, 2009. "Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1368-1376.
    4. Agop, M. & Murgulet, C., 2007. "Ball lightning as a self-organizing process of a plasma–plasma interface and El Naschie’s ε(∞) space–time," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 754-769.
    5. Wang, Guanjun & Cao, Jinde & Lu, Jianquan, 2010. "Outer synchronization between two nonidentical networks with circumstance noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1480-1488.
    6. Chen, Qingjiang & Huo, Ailian, 2009. "The research of a class of biorthogonal compactly supported vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 951-961.
    7. El Naschie, M.S., 2007. "Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 383-387.
    8. Burić, Nikola & Todorović, Kristina & Vasović, Nebojša, 2009. "Dynamics of noisy FitzHugh–Nagumo neurons with delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2405-2413.
    9. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    10. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 91-102.
    11. Burić, Nikola & Todorović, Kristina & Vasović, Nebojša, 2009. "Exact synchronization of noisy bursting neurons with coupling delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1127-1135.
    12. Alimohammady, Mohsen & Esmaeli, Abdolreza & Saadati, Reza, 2009. "Completeness results in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 765-769.
    13. de Souza, Jeferson & Duarte Queirós, Sílvio M., 2009. "Effective multifractal features of high-frequency price fluctuations time series and ℓ-variability diagrams," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2512-2521.
    14. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.
    15. Khrennikov, Andrei Yu., 2009. "Gene expression from polynomial dynamics in the 2-adic information space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 341-347.
    16. Ekici, Erdal & Noiri, Takashi, 2009. "Decompositions of continuity, α-continuity and AB-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2055-2061.
    17. El Naschie, M.S., 2008. "Extended renormalizations group analysis for quantum gravity and Newton’s gravitational constant," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 425-431.
    18. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
    19. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    20. Goldfain, Ervin, 2008. "Critical behavior in continuous dimension, ε∞ theory and particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 928-935.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:727-734. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.