Unveiling Extreme Events in a Nonlinear Chaotic System: Numerical and Experimental Realizations

We investigate a third-order autonomous nonlinear dynamical system and demonstrate that significant variations in system parameters can give rise to Extreme Events (EEs) — rare, large-amplitude deviations from typical system behavior. The occurrence of these EEs is validated through bifurcation analysis, which identifies overlapping regions where the system’s amplitude crosses a critical threshold, clearly demarcating parameter regimes associated with extreme dynamics. Numerical simulations are supported by time-series analysis and corresponding probability distribution functions, both of which confirm the presence and recurrence of EEs. Additionally, a comprehensive two-parameter scan reveals regions of chaotic and quasi-periodic dynamics, enabling precise identification of parameter ranges where extreme behavior emerges. To further validate the numerical results, we implement the system in the experimental laboratory realization. The experimental realizations closely replicate the model dynamics, providing strong evidence for the occurrence of EEs and corroborating the numerical predictions.