Fractional-Order Chaotic Vallis System Under Heavy-Tailed <i>q</i> -Gaussian Noise: Estimation and Simulation

The classical chaotic Vallis system has attracted considerable attention in the field of oceanography, particularly for studies of the El Niño/Southern Oscillation (ENSO) phenomenon. Recent works have examined the stability and solutions of the Vallis system; however, these studies have not incorporated randomness, nor has a noise distribution been considered. To address this gap, we investigate the fractional-order Vallis system under heavy-tailed [Formula: see text]-Gaussian noise, with parameters estimated using the Extended Kalman Filter (EKF) enhanced by a Wavelet Denoising (WD) algorithm. The proposed EKF-WD approach reduces bias in parameter estimation of the fractional-order Vallis system, yielding more accurate results than the classical EKF method. Empirical findings demonstrate the high accuracy of the EKF-WD method across several distribution subclasses. This methodology is expected to support researchers in simulation studies of the ENSO phenomenon, particularly those incorporating non-Gaussian noise in chaotic attractors.