IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v352y2005i2p309-334.html
   My bibliography  Save this article

Classical harmonic oscillator with multiplicative noise

Author

Listed:
  • Gitterman, M.

Abstract

The first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises. A detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study. In both cases the second moments are unstable for the sufficient large noise strength. The difference appears in the stability conditions of the first moments which can diverge already for white noise for the random damping and only for color noise for the random frequency.

Suggested Citation

  • Gitterman, M., 2005. "Classical harmonic oscillator with multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 309-334.
  • Handle: RePEc:eee:phsmap:v:352:y:2005:i:2:p:309-334
    DOI: 10.1016/j.physa.2005.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105000269
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2005.01.008?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.

    Citations

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


    Cited by:

    1. Du, Yuru & Meng, Lin & Lin, Lifeng & Wang, Huiqi, 2024. "Resonant behaviors of two coupled fluctuating-frequency oscillators with tempered Mittag-Leffler memory kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    2. Lin, Lifeng & Lin, Tianzhen & Zhang, Ruoqi & Wang, Huiqi, 2023. "Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    4. Lin, Lifeng & He, Minyue & Wang, Huiqi, 2022. "Collective resonant behaviors in two coupled fluctuating-mass oscillators with tempered Mittag-Leffler memory kernel," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Anatoliy Pogorui & Anatoly Swishchuk & Ramón M. Rodríguez-Dagnino & Alexander Sarana, 2023. "Cox-Based and Elliptical Telegraph Processes and Their Applications," Risks, MDPI, vol. 11(7), pages 1-15, July.
    6. Tian, Yan & He, Guitian & Liu, Zhibin & Zhong, Linfeng & Yang, Xinping & Stanley, H. Eugene & Tu, Zhe, 2021. "The impact of memory effect on resonance behavior in a fractional oscillator with small time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    7. Chen, Xi & Luo, Maokang & Zhong, Yangfan & Zhang, Lu, 2022. "Collective dynamic behaviors of a general adjacent coupled chain in both unconfined and confined spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    8. Berman, Michael & Cederbaum, Lorenz S., 2018. "Fractional driven-damped oscillator and its general closed form exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 744-762.
    9. Guo, Yong-Feng & Shen, Ya-Jun & Tan, Jian-Guo, 2015. "Effects of colored noise and external periodic force on the time derivative of information entropy for a damped harmonic oscillator," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 20-26.
    10. He, Lifang & Wu, Xia & Zhang, Gang, 2020. "Stochastic resonance in coupled fractional-order linear harmonic oscillators with damping fluctuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    11. You, Pinlong & Lin, Lifeng & Wang, Huiqi, 2020. "Cooperative mechanism of generalized stochastic resonance in a time-delayed fractional oscillator with random fluctuations on both mass and damping," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

    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:phsmap:v:352:y:2005:i:2:p:309-334. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.