IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v616y2023ics0378437123001383.html
   My bibliography  Save this article

A note on microlocal kernel design for some slow–fast stochastic differential equations with critical transitions and application to EEG signals

Author

Listed:
  • Hamzi, Boumediene
  • Owhadi, Houman
  • Paillet, Léo

Abstract

This technical note presents an extension of kernel model decomposition (KMD) for detecting critical transitions in some fast–slow random dynamical systems. The approach rests upon modifying KMD for reconstructing an observable by using a novel data-based time-frequency-phase kernel that allows to approximate signals with critical transitions. In particular, we apply the developed method for approximating the solution and detecting critical transitions in some prototypical slow–fast SDEs with critical transitions. We also apply it to detecting seizures in a multi-scale mesoscale nine-dimensional SDE model of brain activity.

Suggested Citation

  • Hamzi, Boumediene & Owhadi, Houman & Paillet, Léo, 2023. "A note on microlocal kernel design for some slow–fast stochastic differential equations with critical transitions and application to EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    • Handle: RePEc:eee:phsmap:v:616:y:2023:i:c:s0378437123001383
    DOI: 10.1016/j.physa.2023.128583
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123001383
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.128583?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. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
    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. Richter, Andries & Dakos, Vasilis, 2015. "Profit fluctuations signal eroding resilience of natural resources," Ecological Economics, Elsevier, vol. 117(C), pages 12-21.
    2. Karimi Rahjerdi, Bahareh & Ramamoorthy, Ramesh & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Jafari, Sajad, 2022. "Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. John M Drake & Tobias S Brett & Shiyang Chen & Bogdan I Epureanu & Matthew J Ferrari & Éric Marty & Paige B Miller & Eamon B O’Dea & Suzanne M O’Regan & Andrew W Park & Pejman Rohani, 2019. "The statistics of epidemic transitions," PLOS Computational Biology, Public Library of Science, vol. 15(5), pages 1-14, May.
    4. James J Elser & Timothy J Elser & Stephen R Carpenter & William A Brock, 2014. "Regime Shift in Fertilizer Commodities Indicates More Turbulence Ahead for Food Security," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-7, May.
    5. Roland Clift & Sarah Sim & Henry King & Jonathan L. Chenoweth & Ian Christie & Julie Clavreul & Carina Mueller & Leo Posthuma & Anne-Marie Boulay & Rebecca Chaplin-Kramer & Julia Chatterton & Fabrice , 2017. "The Challenges of Applying Planetary Boundaries as a Basis for Strategic Decision-Making in Companies with Global Supply Chains," Sustainability, MDPI, vol. 9(2), pages 1-23, February.
    6. Darrell Jiajie Tay & Chung-I Chou & Sai-Ping Li & Shang You Tee & Siew Ann Cheong, 2016. "Bubbles Are Departures from Equilibrium Housing Markets: Evidence from Singapore and Taiwan," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-13, November.
    7. Fushing, Hsieh & Jordà, Òscar & Beisner, Brianne & McCowan, Brenda, 2014. "Computing systemic risk using multiple behavioral and keystone networks: The emergence of a crisis in primate societies and banks," International Journal of Forecasting, Elsevier, vol. 30(3), pages 797-806.
    8. Dur, Gaël & Won, Eun-Ji & Han, Jeonghoon & Lee, Jae-Seong & Souissi, Sami, 2021. "An individual-based model for evaluating post-exposure effects of UV-B radiation on zooplankton reproduction," Ecological Modelling, Elsevier, vol. 441(C).
    9. Martin Lindegren & Vasilis Dakos & Joachim P Gröger & Anna Gårdmark & Georgs Kornilovs & Saskia A Otto & Christian Möllmann, 2012. "Early Detection of Ecosystem Regime Shifts: A Multiple Method Evaluation for Management Application," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    10. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    11. Quentin Remy & Julius Hohlfeld & Maxime Vergès & Yann Le Guen & Jon Gorchon & Grégory Malinowski & Stéphane Mangin & Michel Hehn, 2023. "Accelerating ultrafast magnetization reversal by non-local spin transfer," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    12. Hu, Jiang-Hong & Xue, Ya-Kui & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2016. "Global dynamics of a predator–prey system modeling by metaphysiological approach," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 369-384.
    13. Jinxiao Duan & Guanwen Zeng & Nimrod Serok & Daqing Li & Efrat Blumenfeld Lieberthal & Hai-Jun Huang & Shlomo Havlin, 2023. "Spatiotemporal dynamics of traffic bottlenecks yields an early signal of heavy congestions," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    14. Vasilis Dakos & Stephen R Carpenter & William A Brock & Aaron M Ellison & Vishwesha Guttal & Anthony R Ives & Sonia Kéfi & Valerie Livina & David A Seekell & Egbert H van Nes & Marten Scheffer, 2012. "Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-20, July.
    15. Wang, Gang-Jin & Xie, Chi, 2013. "Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1418-1428.
    16. Domenico Di Gangi & Fabrizio Lillo & Davide Pirino, 2015. "Assessing systemic risk due to fire sales spillover through maximum entropy network reconstruction," Papers 1509.00607, arXiv.org, revised Jul 2018.
    17. Nils Bertschinger & Oliver Pfante, 2020. "Early Warning Signs of Financial Market Turmoils," JRFM, MDPI, vol. 13(12), pages 1-24, November.
    18. Christian Meisel & Andreas Klaus & Christian Kuehn & Dietmar Plenz, 2015. "Critical Slowing Down Governs the Transition to Neuron Spiking," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-20, February.
    19. Zeng, Chunhua & Wang, Hua, 2012. "Noise and large time delay: Accelerated catastrophic regime shifts in ecosystems," Ecological Modelling, Elsevier, vol. 233(C), pages 52-58.
    20. Hayette Gatfaoui & Isabelle Nagot & Philippe de Peretti, 2016. "Are critical slowing down indicators useful to detect financial crises?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01339815, HAL.

    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:phsmap:v:616:y:2023:i:c:s0378437123001383. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.