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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
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    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).
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    Cited by:

    1. Thamilmaran, K. & Bhagyaraj, T. & Sabarathinam, S., 2024. "Extreme events in a damped Korteweg–de Vries (KdV) autonomous system: A comprehensive analysis," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. Kamdjeu Kengne, Léandre & Folifack Signing, Vitrice Ruben & Rossi Sebastiano, Davide & Wafo Tekam, Raoul Blaise & Ngamsa Tegnitsap, Joakim Vianney & Zhao, Manyu & Bao, Qingshi & Kengne, Jacques & Vald, 2025. "Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).

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