IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007397.html
   My bibliography  Save this article

Certification of almost global phase synchronization of all-to-all coupled phase oscillators

Author

Listed:
  • Kudeyt, Mahmut
  • Kıvılcım, Ayşegül
  • Köksal-Ersöz, Elif
  • İlhan, Ferruh
  • Karabacak, Özkan

Abstract

Coupled oscillators may exhibit almost global phase synchronization, namely their phases tend to asymptotically overlap for almost all initial conditions. We consider certification of this property using Rantzer’s dual Lyapunov approach with sum of squares (SOS) programming. To this aim, we use a stereographic transformation from a hypertorus to an Euclidean space. For the case of all-to-all coupling, this transformation converts the problem of certifying stability into the problem of certifying divergence of almost all solutions to infinity. We show that the latter can be solved using a polynomial Lyapunov density, which can be constructed via SOS programming. This leads to the certification of almost global phase synchronization of all-to-all coupled phase oscillators. We apply our method to an example of coupled phase oscillators and to an example of coupled van der Pol oscillators, and show that it can support the existing tools of local stability analysis by ensuring almost global phase synchronization.

Suggested Citation

  • Kudeyt, Mahmut & Kıvılcım, Ayşegül & Köksal-Ersöz, Elif & İlhan, Ferruh & Karabacak, Özkan, 2023. "Certification of almost global phase synchronization of all-to-all coupled phase oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007397
    DOI: 10.1016/j.chaos.2023.113838
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007397
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113838?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. Lotrič, Maja Bračič & Stefanovska, Aneta, 2000. "Synchronization and modulation in the human cardiorespiratory system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 451-461.
    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. Ekaterina I. Borovkova & Vladimir I. Ponomarenko & Anatoly S. Karavaev & Elizaveta S. Dubinkina & Mikhail D. Prokhorov, 2023. "Method of Extracting the Instantaneous Phases and Frequencies of Respiration from the Signal of a Photoplethysmogram," Mathematics, MDPI, vol. 11(24), pages 1-14, December.
    2. López-Mancilla, Didier & Cruz-Hernández, César, 2008. "Output synchronization of chaotic systems under nonvanishing perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1172-1186.
    3. Ponomarenko, V.I. & Prokhorov, M.D. & Bespyatov, A.B. & Bodrov, M.B. & Gridnev, V.I., 2005. "Deriving main rhythms of the human cardiovascular system from the heartbeat time series and detecting their synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1429-1438.
    4. Yuanzhao Zhang & Maxime Lucas & Federico Battiston, 2023. "Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes," Nature Communications, Nature, vol. 14(1), pages 1-8, 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:174:y:2023:i:c:s0960077923007397. 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.