IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v192y2025ics096007792500013x.html
   My bibliography  Save this article

Extreme events at the onset of epileptic-like intermittent activity of FitzHugh–Nagumo oscillators on small-world networks

Author

Listed:
  • Cubillos-Cornejo, Javier
  • Mendoza, Miguel Escobar
  • Bordeu, Ignacio

Abstract

In this work, we explore the influence of coupling strength, network size, and randomness on the collective dynamics of FitzHugh–Nagumo oscillators on complex networks. Using Watts–Strogatz small-world network connectivities, we identify four distinct dynamical phases: chaotic, intermittent, partially synchronized, and fully synchronized. The intermittent phase is characterized by the coexistence of chaotic behavior and chimera states, reminiscent of epileptic-seizure-related (ESR) intermittency observed in the brain. We analyze the inter-spike intervals of the individual oscillators, and the existence, duration, and frequency of ESR events as a function of the system parameters. Furthermore, we study the transitions into and out of the intermittent phase and show that peaks in the probability of extreme events – short transients of anomalously high synchronization – precede the transitions from chaos to intermittency and from partial to full synchronization. These transitions are followed by significant changes in the maximum Lyapunov exponent and Kaplan–Yorke dimension. Finally, we discuss how the coupling strength and network properties can be leveraged to control the system’s state and the potential applications of extreme event analysis in the study of neural data.

Suggested Citation

  • Cubillos-Cornejo, Javier & Mendoza, Miguel Escobar & Bordeu, Ignacio, 2025. "Extreme events at the onset of epileptic-like intermittent activity of FitzHugh–Nagumo oscillators on small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s096007792500013x
    DOI: 10.1016/j.chaos.2025.116000
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792500013X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116000?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. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    2. Alexandros Rontogiannis & Astero Provata, 2021. "Chimera states in FitzHugh–Nagumo networks with reflecting connectivity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(5), pages 1-12, May.
    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. Konstantinos Antoniadis & Kostas Zafiropoulos & Vasiliki Vrana, 2016. "A Method for Assessing the Performance of e-Government Twitter Accounts," Future Internet, MDPI, vol. 8(2), pages 1-18, April.
    2. Yue Chen & Xiaojian Niu & Yan Zhang, 2019. "Exploring Contrarian Degree in the Trading Behavior of China's Stock Market," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    3. Fateev, I. & Polezhaev, A., 2024. "Chimera states in a lattice of superdiffusively coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Del Giudice, Alfonso & Foglia, Matteo & Gianfrancesco, Igor, 2025. "Investor networks and social innovation: A stakeholder network analysis of Social Impact Bonds," International Review of Economics & Finance, Elsevier, vol. 99(C).
    5. Daniel Felix Ahelegbey & Luis Carvalho & Eric D. Kolaczyk, 2020. "A Bayesian Covariance Graph And Latent Position Model For Multivariate Financial Time Series," DEM Working Papers Series 181, University of Pavia, Department of Economics and Management.
    6. Lawford, Steve & Mehmeti, Yll, 2020. "Cliques and a new measure of clustering: With application to U.S. domestic airlines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    7. Tsonis, Anastasios A. & Swanson, Kyle L. & Wang, Geli, 2008. "Estimating the clustering coefficient in scale-free networks on lattices with local spatial correlation structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5287-5294.
    8. Pollner, Péter & Palla, Gergely & Vicsek, Tamás, 2010. "Clustering of tag-induced subgraphs in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5887-5894.
    9. Ahelegbey, Daniel Felix & Billio, Monica & Casarin, Roberto, 2024. "Modeling Turning Points in the Global Equity Market," Econometrics and Statistics, Elsevier, vol. 30(C), pages 60-75.
    10. Ding Ding & Liyan Han & Libo Yin, 2017. "Systemic risk and dynamics of contagion: a duplex inter-bank network," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1435-1445, September.
    11. Pereira, F.B. & Ferreira, R.S. & Alencar, D.S.M. & Alves, T.F.A. & Alves, G.A. & Lima, F.W.S. & Macedo-Filho, A., 2024. "Social dilemmas, network reciprocity, and small-world property," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 655(C).
    12. Zheng, Sen & Zhang, Jie & Jian, Lirong, 2024. "Green technology diffusion mechanism in China's aviation industry cluster based on complex network game model," Energy, Elsevier, vol. 313(C).
    13. Guida, Michele & Maria, Funaro, 2007. "Topology of the Italian airport network: A scale-free small-world network with a fractal structure?," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 527-536.
    14. Elena Agliari & Adriano Barra & Andrea Galluzzi & Marco Alberto Javarone & Andrea Pizzoferrato & Daniele Tantari, 2015. "Emerging Heterogeneities in Italian Customs and Comparison with Nearby Countries," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-24, December.
    15. Ostilli, M., 2024. "Exact results for the Ising model on a small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    16. Hossein Sabzian & Mohammad Ali Shafia & Mehdi Ghazanfari & Ali Bonyadi Naeini, 2020. "Modeling the Adoption and Diffusion of Mobile Telecommunications Technologies in Iran: A Computational Approach Based on Agent-Based Modeling and Social Network Theory," Sustainability, MDPI, vol. 12(7), pages 1-36, April.
    17. Gian Paolo Clemente & Marco Fattore & Rosanna Grassi, 2018. "Structural comparisons of networks and model-based detection of small-worldness," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(1), pages 117-141, April.
    18. Robert Boyer & Denis Boyer & Gilles Laferté, 2007. "La connexion des réseaux comme facteur de changement institutionnel : l'exemple des vins de Bourgogne," PSE Working Papers halshs-00587708, HAL.
    19. Marr, Carsten & Hütt, Marc-Thorsten, 2005. "Topology regulates pattern formation capacity of binary cellular automata on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 641-662.
    20. Bombelli, Alessandro & Santos, Bruno F. & Tavasszy, Lóránt, 2020. "Analysis of the air cargo transport network using a complex network theory perspective," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(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:192:y:2025:i:c:s096007792500013x. 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.