IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921005439.html
   My bibliography  Save this article

Distinctive roles of hysteresis, amplitude death and oscillation death in generating fast-slow phenomena in parametrically and externally excited systems

Author

Listed:
  • Xiao, Junyan
  • Chen, Zhangyao
  • Bi, Qinsheng
  • Zou, Yong
  • Guan, Shuguang

Abstract

Fast-slow phenomena are often referred to as time series showing clearly separated time scales of alternations between consecutive high-frequency large-amplitude oscillations and much smaller amplitudes or much more infrequent or quiescent intervals, which can be observed in many nonlinear systems. In this work, we show distinctive roles of hysteresis, amplitude death and oscillation death mechanisms in generating fast-slow switching behavior by using the paradigmatic models of Duffing and Van der Pol systems which are driven by both parametric and external excitations for the case when the frequencies of excitations are 1:1 and 1:2 rationally correlated. In the Duffing system, we show that hysteresis is the main mechanism to generate fast-slow behavior and the fast oscillations are resulted from the transient processes between different steady states. On the other hand, in the Van der Pol system, amplitude death and oscillation death are the fundamental mechanisms because of Hopf bifurcation. In this case, fast oscillations mainly correspond to the limit cycles, while slow quiescent intervals are due to the stable fixed points. In addition, we provide a rather simple model to implement responding lags of Van der Pol oscillators to the same external forcing, resulting in fast-slow switching relaying scenarios among subsystems. All theoretical results have been confirmed precisely by numerical simulations.

Suggested Citation

  • Xiao, Junyan & Chen, Zhangyao & Bi, Qinsheng & Zou, Yong & Guan, Shuguang, 2021. "Distinctive roles of hysteresis, amplitude death and oscillation death in generating fast-slow phenomena in parametrically and externally excited systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005439
    DOI: 10.1016/j.chaos.2021.111189
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921005439
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111189?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. J. R. Leeman & D. M. Saffer & M. M. Scuderi & C. Marone, 2016. "Laboratory observations of slow earthquakes and the spectrum of tectonic fault slip modes," Nature Communications, Nature, vol. 7(1), pages 1-6, September.
    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. Danjin Zhang & Youhua Qian, 2023. "Bursting Oscillations in General Coupled Systems: A Review," Mathematics, MDPI, vol. 11(7), pages 1-16, April.

    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. Huihui Weng & Jean-Paul Ampuero, 2022. "Integrated rupture mechanics for slow slip events and earthquakes," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    2. Thomas H. W. Goebel & Valerian Schuster & Grzegorz Kwiatek & Kiran Pandey & Georg Dresen, 2024. "A laboratory perspective on accelerating preparatory processes before earthquakes and implications for foreshock detectability," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    3. Sara Beth L. Cebry & Chun-Yu Ke & Srisharan Shreedharan & Chris Marone & David S. Kammer & Gregory C. McLaskey, 2022. "Creep fronts and complexity in laboratory earthquake sequences illuminate delayed earthquake triggering," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. David C. Bolton & Chris Marone & Demian Saffer & Daniel T. Trugman, 2023. "Foreshock properties illuminate nucleation processes of slow and fast laboratory earthquakes," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    5. Peng Dong & Kaiwen Xia & Ying Xu & Derek Elsworth & Jean-Paul Ampuero, 2023. "Laboratory earthquakes decipher control and stability of rupture speeds," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    6. Prabhav Borate & Jacques Rivière & Chris Marone & Ankur Mali & Daniel Kifer & Parisa Shokouhi, 2023. "Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    7. David S. Kammer & Gregory C. McLaskey & Rachel E. Abercrombie & Jean-Paul Ampuero & Camilla Cattania & Massimo Cocco & Luca Dal Zilio & Georg Dresen & Alice-Agnes Gabriel & Chun-Yu Ke & Chris Marone &, 2024. "Earthquake energy dissipation in a fracture mechanics framework," Nature Communications, Nature, vol. 15(1), pages 1-9, December.

    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:150:y:2021:i:c:s0960077921005439. 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.