IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v30y2006i5p1034-1047.html
   My bibliography  Save this article

Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

Author

Listed:
  • Gandhimathi, V.M.
  • Murali, K.
  • Rajasekar, S.

Abstract

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude f of the applied periodic force is varied cross-well motion is realized above a critical value (fc) of f. This is found for all the forces except the modulus of sine and rectified sinusoidal forces. For fixed values of angular frequency ω of the periodic forces, fc is minimum for square wave and maximum for asymmetric saw-tooth wave. fc is found to scale as Ae0.75ω+B where A and B are constants. Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. The stochastic resonance behaviour is quantized using power spectrum, signal-to-noise ratio, mean residence time and distribution of normalized residence times. The logarithmic plot of mean residence time τMR against 1/(D−Dc) where D is the intensity of the noise and Dc is the value of D at which cross-well motion is initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity D=Dmax at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus of sine wave and rectified sine wave, the SNR peaks at a value of D for which sum of τMR in two wells of the potential of the system is half of the period of the driving force. For the chosen values of f and ω, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and rectified sinusoidal waves. The values of Dc at which cross-well behaviour is initiated and Dmax are found to depend on the shape of the periodic forces.

Suggested Citation

  • Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2006. "Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1034-1047.
  • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1034-1047
    DOI: 10.1016/j.chaos.2005.09.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905008842
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.09.046?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. Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
    2. Sinha, Sitabhra, 1999. "Noise-free stochastic resonance in simple chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 204-214.
    3. Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2005. "Stochastic resonance in overdamped two coupled anharmonic oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 99-116.
    4. Carusela, M.F. & Codnia, J. & Romanelli, L., 2003. "Stochastic resonance: numerical and experimental devices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 415-420.
    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. Zhu, Jinjie & Zhao, Feng & Li, Yang & Liu, Xianbin, 2024. "Rotational stochastic resonance in multistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    2. Srinivasan, K. & Thamilmaran, K. & Venkatesan, A., 2009. "Effect of nonsinusoidal periodic forces in Duffing oscillator: Numerical and analog simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 319-330.
    3. Cang, Shijian & Zhao, Gehang & Wang, Zenghui & Chen, Zengqiang, 2022. "Global structures of clew-shaped conservative chaotic flows in a class of 3D one-thermostat systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    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. Chun Zhang & Tao Yang & Shi-Xian Qu, 2021. "Impact of time delays and environmental noise on the extinction of a population dynamics model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-16, November.
    2. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    3. Patterson, G.A. & Goya, A.F. & Fierens, P.I. & Ibáñez, S.A. & Grosz, D.F., 2010. "Experimental investigation of noise-assisted information transmission and storage via stochastic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1965-1970.
    4. Lumi, Neeme & Laas, Katrin & Mankin, Romi, 2015. "Rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 109-118.
    5. Han, Chunxiao & Qin, Yingmei & Qin, Qing & Wang, Ruofan & Lu, Meili & Zhao, Jia & Che, Yanqiu, 2019. "Vibrational resonance without tuning in a neuronal parallel array," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 204-210.
    6. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    8. Morozov, Andrew Yu. & Almutairi, Dalal & Petrovskii, Sergei V. & Lai, Ying-Cheng, 2023. "Long transients in discontinuous time-discrete models of population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Vladislav Soukhovolsky & Anton Kovalev & Yulia Ivanova & Olga Tarasova, 2023. "Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    10. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    11. Mi, Li-Na & Guo, Yong-Feng & Zhang, Meng & Zhuo, Xiao-Jing, 2023. "Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    12. Varughese, M.M. & Fatti, L.P., 2008. "Incorporating environmental stochasticity within a biological population model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 115-129.
    13. Bekoa, D.J. Owono & Kenfack, W. Fokou & Siewe, M. Siewe, 2022. "Dynamics of saline oscillator under sinusoidal and bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    14. Alsulami, Amer & Petrovskii, Sergei, 2023. "A model of mass extinction accounting for the differential evolutionary response of species to a climate change," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    15. Tian, Rongrong & Wei, Jinlong & Wu, Jiang-Lun, 2021. "On a generalized population dynamics equation with environmental noise," Statistics & Probability Letters, Elsevier, vol. 168(C).

    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:30:y:2006:i:5:p:1034-1047. 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.