IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics096007792400420x.html
   My bibliography  Save this article

Emergent rhythmicity and control in a stochastic trirhythmic system

Author

Listed:
  • Guo, Qin
  • Han, Ping
  • Zhang, Hongxia
  • Feng, Jinqian
  • Su, Jin

Abstract

In the trirhythmic system, the coexistence of three stable limit cycles (LCs) renders the system highly sensitive to subtle input variations. This study meticulously examines how system parameters, filtered feedback control, and Gaussian perturbations impact the system’s bifurcation behaviors. Using the harmonic decomposition method, the deterministic bifurcation behaviors of the trirhythmic system under filtered feedback control are explored. By applying the stochastic averaging method, the stationary probability density function(SPDF) of the system’s amplitude is derived, further facilitating the construction of one-parameter and two-parameter bifurcation diagrams. These diagrams contribute to a thorough understanding of the multirhythmic oscillation phenomenon within the system. It should be noted that the presence of noise with higher intensity significantly disrupts the rhythmicity of the system, while the introduction of filtered feedback control ensures multirhythmic oscillation to a large extent. Furthermore, the magnitudes of parameters α and β profoundly influence the amplitude distribution range: larger values correspond to narrower amplitude distribution ranges, whereas smaller values result in broader distributions. The proposed method in this paper exhibits high precision, and numerical results validate the accuracy of the theoretical analysis.

Suggested Citation

  • Guo, Qin & Han, Ping & Zhang, Hongxia & Feng, Jinqian & Su, Jin, 2024. "Emergent rhythmicity and control in a stochastic trirhythmic system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s096007792400420x
    DOI: 10.1016/j.chaos.2024.114868
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792400420X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114868?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. Yonkeu, R. Mbakob, 2023. "Stochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2020. "Noise-induced shifts in dynamics of multi-rhythmic population SIP-model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    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. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2022. "Regular and chaotic variability caused by random disturbances in a predator–prey system with disease in predator," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Sk, Nazmul & Mondal, Bapin & Thirthar, Ashraf Adnan & Alqudah, Manar A. & Abdeljawad, Thabet, 2023. "Bistability and tristability in a deterministic prey–predator model: Transitions and emergent patterns in its stochastic counterpart," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Ramazanov, Ibadulla R. & Korneev, Ivan A. & Vadivasova, Tatiana E. & Slepnev, Andrei V., 2024. "Dynamics of two coupled van der Pol–Mathieu oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 182(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:chsofr:v:183:y:2024:i:c:s096007792400420x. 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.