Abstract
In this study, we investigate the occurrence of dragon-king extreme events in a three-dimensional autonomous Shimizu–Morioka oscillator. We observe that the bounded chaotic oscillations transition into large amplitude extreme events at a critical value of the system control parameter triggered by an interior crisis. These extreme events exhibit a unique distribution characterized by the probability distribution function. We performed laboratory experiments and conducted rigorous numerical simulations on the Shimizu–Morioka oscillator to validate our findings. The results from both approaches are in excellent agreement and confirm extreme behavior in this autonomous system. Our study represents the first comprehensive investigation of extreme events in the Shimizu–Morioka oscillator, integrating experimental observations and numerical simulations. Also, we observed the dragon-king extreme events in both experimental and numerical studies. These findings enhance our understanding of extreme events and their potential applications in chaos-based dynamical systems, contributing to advancing this field.
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