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Extreme events in a damped Korteweg–de Vries (KdV) autonomous system: A comprehensive analysis

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  • Thamilmaran, K.
  • Bhagyaraj, T.
  • Sabarathinam, S.

Abstract

This manuscript explores extreme events in a three-dimensional, damped Korteweg–de Vries (KdV) autonomous system that is derived from the jerk system with a modified basin. Through rigorous stability analysis, we identify the extreme events, confirmed using phase portraits, Poincaré return maps, time series, and probability distribution functions. The Dragon-king phenomenon is obtained and self-organised criticality is discussed. The regime of extreme events in a wide parameter range was obtained through two-parameter scanning. The analog circuit was constructed to mimicking dynamics of damped KdV equation and demonstrated in real-time hardware experiment as well as PSpice simulation. The experimental results show excellent agreement with the numerically obtained results. This study is the first comprehensive examination of extreme events in the damped KdV system, highlighting their nature and potential applications in chaos-based dynamical systems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008890
    DOI: 10.1016/j.chaos.2024.115337
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    References listed on IDEAS

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    1. Ira Didenkulova & Roger Grimshaw & Alexey Slunyaev & Stefano Tinti, 2016. "Advances in nonlinear wave research for hazard warning and mitigation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(2), pages 431-436, November.
    2. Chlouverakis, Konstantinos E. & Sprott, J.C., 2006. "Chaotic hyperjerk systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 739-746.
    3. Xing-Yun Zou & Xin-Yu Peng & Xin-Xin Zhao & Chun-Ping Chang, 2023. "The impact of extreme weather events on water quality: international evidence," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 115(1), pages 1-21, January.
    4. 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).
    5. 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).
    6. Ahmed Daeli & Salman Mohagheghi, 2022. "Power Grid Infrastructural Resilience against Extreme Events," Energies, MDPI, vol. 16(1), pages 1-17, December.
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    1. 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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