Hybrid Lyapunov–Vision Framework for Chaos Identification in Fractional-Order Nonlinear Dynamics

This study presents a unified computational framework for detecting chaotic behavior in a fractional-order Lorenz system by combining Lyapunov-based dynamical analysis with modern machine learning methods. The fractional-order system is simulated over a wide range of the control parameter, and the corresponding Lyapunov spectrum is computed to identify chaotic and non-chaotic regimes. These time-domain trajectories are transformed into high-resolution wavelet scalogram images, enabling a vision-based representation of fractional-order dynamics. The resulting image dataset is classified using both a Vision Transformer (ViT) model and a Support Vector Machine (SVM) classifier built on ViT-extracted feature embeddings. Experimental results demonstrate that the ViT model achieves near-perfect discrimination between chaotic and non-chaotic patterns, with an accuracy of 0.9627, a Cohen’s kappa of 0.920, and an MCC of 0.949. The SVM classifier yields even higher performance, achieving an accuracy of 0.9776, a kappa coefficient of 0.955, and an MCC of 0.955. ROC analyses confirm that both models reach an AUC of 1.00, indicating excellent separability between the two classes. The findings show that wavelet-based image encoding combined with transformer architectures provides a powerful and generalizable approach for chaos detection in fractional-order nonlinear systems. This integrated methodology offers a scalable solution for automated analysis of complex dynamical behavior and establishes a bridge between classical chaos theory and state-of-the-art deep learning models.