IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2199-d1434401.html
   My bibliography  Save this article

Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

Author

Listed:
  • Irina Bashkirtseva

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

Abstract

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement.

Suggested Citation

  • Irina Bashkirtseva, 2024. "Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2199-:d:1434401
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2199/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2199/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.
    2. Sun, Yahui & Hong, Ling & Jiang, Jun, 2017. "Stochastic sensitivity analysis of nonautonomous nonlinear systems subjected to Poisson white noise," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 508-515.
    Full references (including those not matched with items on IDEAS)

    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. Jungeilges, Jochen & Pavletsov, Makar & Perevalova, Tatyana, 2022. "Noise-induced behavioral change driven by transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Belyaev, Alexander & Bashkirtseva, Irina & Ryashko, Lev, 2021. "Stochastic variability of regular and chaotic dynamics in 2D metapopulation model," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Lev Ryashko & Irina Bashkirtseva, 2022. "Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction," Mathematics, MDPI, vol. 10(6), pages 1-11, March.

    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:gam:jmathe:v:12:y:2024:i:14:p:2199-:d:1434401. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.