IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v145y2021ics0960077921001685.html
   My bibliography  Save this article

Topological phase transition in the periodically forced Kuramoto model

Author

Listed:
  • Wright, E.A.P.
  • Yoon, S.
  • Mendes, J.F.F.
  • Goltsev, A.V.

Abstract

A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18, 043128 (2008)], identifying all bifurcations within the model. We show that the phase diagram predicted by this analysis is incomplete. Our numerical analysis of the equations reveals that the model can also undergo an abrupt phase transition from oscillations to wobbly rotations of the order parameter under increasing field frequency or decreasing field strength. This transition was not revealed by bifurcation analysis because it is not caused by a bifurcation, and can neither be classified as first nor second order since it does not display critical phenomena characteristic of either transition. We discuss the topological origin of this transition and show that it is determined by a singular point in the order-parameter space.

Suggested Citation

  • Wright, E.A.P. & Yoon, S. & Mendes, J.F.F. & Goltsev, A.V., 2021. "Topological phase transition in the periodically forced Kuramoto model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001685
    DOI: 10.1016/j.chaos.2021.110816
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921001685
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110816?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. Nikita A. Olekhno & Egor I. Kretov & Andrei A. Stepanenko & Polina A. Ivanova & Vitaly V. Yaroshenko & Ekaterina M. Puhtina & Dmitry S. Filonov & Barbara Cappello & Ladislau Matekovits & Maxim A. Gorl, 2020. "Topological edge states of interacting photon pairs emulated in a topolectrical circuit," Nature Communications, Nature, vol. 11(1), pages 1-8, December.
    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. Dharma Raj Khatiwada, 2022. "Numerical Solution of Finite Kuramoto Model with Time-Dependent Coupling Strength: Addressing Synchronization Events of Nature," Mathematics, MDPI, vol. 10(19), pages 1-10, October.

    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. Ren, Boquan & Kartashov, Yaroslav V. & Wang, Hongguang & Li, Yongdong & Zhang, Yiqi, 2023. "Floquet topological insulators with hybrid edges," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Weixuan Zhang & Fengxiao Di & Xingen Zheng & Houjun Sun & Xiangdong Zhang, 2023. "Hyperbolic band topology with non-trivial second Chern numbers," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    3. Weixuan Zhang & Hao Yuan & Haiteng Wang & Fengxiao Di & Na Sun & Xingen Zheng & Houjun Sun & Xiangdong Zhang, 2022. "Observation of Bloch oscillations dominated by effective anyonic particle statistics," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    4. Deyuan Zou & Tian Chen & Wenjing He & Jiacheng Bao & Ching Hua Lee & Houjun Sun & Xiangdong Zhang, 2021. "Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    5. Weixuan Zhang & Hao Yuan & Na Sun & Houjun Sun & Xiangdong Zhang, 2022. "Observation of novel topological states in hyperbolic lattices," Nature Communications, Nature, vol. 13(1), pages 1-10, 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:145:y:2021:i:c:s0960077921001685. 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.