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

Author

Listed:
  • 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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