IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v180y2024ics0960077924001334.html
   My bibliography  Save this article

Dynamical instabilities cause extreme events in a theoretical Brusselator model

Author

Listed:
  • Manivelan, S.V.
  • Sabarathinam, S.
  • Thamilmaran, K.
  • Manimehan, I.

Abstract

In this manuscript, we report the rich dynamics of the theoretical Brusselator model, which is driven by a periodic external force. We observed and confirmed a variety of dynamical features with the most interesting extreme events behaviour in the proposed system. The dynamics of the system are characterised by the bifurcation diagram, Lyapunov exponent, phase portraits, and time series segments. The extreme events behaviour is characterised by the probability distribution function, instantaneous phase calculation, and Poincaré return map. Real-time hardware experiments were carried out using an analog electronic circuit, and the outcomes of the experimental observations were confirmed with the numerically obtained results. To the best of our knowledge, we believe that it is for the first time that the occurrence of extreme events has been reported using both the numerical simulation studies and the real-time analog electronic experimental observations on this forced Brusselator chemical model.

Suggested Citation

  • Manivelan, S.V. & Sabarathinam, S. & Thamilmaran, K. & Manimehan, I., 2024. "Dynamical instabilities cause extreme events in a theoretical Brusselator model," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001334
    DOI: 10.1016/j.chaos.2024.114582
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924001334
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114582?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. Anders Johansen & Didier Sornette, 2010. "Shocks, Crashes and Bubbles in Financial Markets," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 53(2), pages 201-253.
    2. Sudharsan, S. & Venkatesan, A. & Muruganandam, P. & Senthilvelan, M., 2022. "Suppression of extreme events and chaos in a velocity-dependent potential system with time-delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Thangavel, Bhagyaraj & Srinivasan, Sabarathinam & Kathamuthu, Thamilmaran, 2021. "Extreme events in a forced BVP oscillator: Experimental and numerical studies," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Milovanov, Alexander V. & Rasmussen, Jens Juul & Groslambert, Bertrand, 2021. "Black swans, extreme risks, and the e-pile model of self-organized criticality," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, 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. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    2. M. Naresh Kumar & V. Sree Hari Rao, 2015. "A New Methodology for Estimating Internal Credit Risk and Bankruptcy Prediction under Basel II Regime," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 83-102, June.
    3. Wątorek Marcin & Stawiarski Bartosz, 2016. "Log-Periodic Power Law and Generalized Hurst Exponent Analysis in Estimating an Asset Bubble Bursting Time," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 12(3), pages 49-58, October.
    4. Xia Yang & Jing Zhang & Wei-Xin Ren, 2018. "Threshold selection for extreme value estimation of vehicle load effect on bridges," International Journal of Distributed Sensor Networks, , vol. 14(2), pages 15501477187, February.
    5. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    6. Xin Chen & Zhangming Shan & Decai Tang & Biao Zhou & Valentina Boamah, 2023. "Interest rate risk of Chinese commercial banks based on the GARCH-EVT model," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-11, December.
    7. Jian Zhou, 2012. "Extreme risk measures for REITs: a comparison among alternative methods," Applied Financial Economics, Taylor & Francis Journals, vol. 22(2), pages 113-126, January.
    8. Gonzales-Martínez, Rolando, 2008. "Medidas de Riesgo Financiero y una Aplicación a las Variaciones de Depósitos del Sistema Financiero Boliviano [Risk Measures and an Application to the Withdrawals of Deposits in the Bolivian Financ," MPRA Paper 14700, University Library of Munich, Germany.
    9. Fruehwirt, Wolfgang & Hochfilzer, Leonhard & Weydemann, Leonard & Roberts, Stephen, 2021. "Cumulation, crash, coherency: A cryptocurrency bubble wavelet analysis," Finance Research Letters, Elsevier, vol. 40(C).
    10. Mizgier, Kamil J. & Hora, Manpreet & Wagner, Stephan M. & Jüttner, Matthias P., 2015. "Managing operational disruptions through capital adequacy and process improvement," European Journal of Operational Research, Elsevier, vol. 245(1), pages 320-332.
    11. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    12. John Fry & McMillan David, 2015. "Stochastic modelling for financial bubbles and policy," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1002152-100, December.
    13. John Fry, 2014. "Bubbles, shocks and elementary technical trading strategies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-13, January.
    14. Ludovic Tangpi & Shichun Wang, 2022. "Optimal Bubble Riding: A Mean Field Game with Varying Entry Times," Papers 2209.04001, arXiv.org, revised Jan 2024.
    15. Davide Ferrari & Sandra Paterlini, 2009. "The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 3-19, March.
    16. Eling, Martin & Wirfs, Jan Hendrik, 2016. "Cyber Risk: Too Big to Insure? Risk Transfer Options for a mercurial risk class," I.VW HSG Schriftenreihe, University of St.Gallen, Institute of Insurance Economics (I.VW-HSG), volume 59, number 59.
    17. David E. Giles & Qinlu Chen, 2014. "Risk Analysis for Three Precious Metals: An Application of Extreme Value Theory," Econometrics Working Papers 1402, Department of Economics, University of Victoria.
    18. Dey Ashim Kumar & Das Kumer Pial, 2020. "Predicting Federal Funds Rate Using Extreme Value Theory," Stochastics and Quality Control, De Gruyter, vol. 35(1), pages 1-15, June.
    19. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    20. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.

    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:180:y:2024:i:c:s0960077924001334. 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.