Abstract
Fractional-order chaotic systems describe complex dynamic processes with memory effects and long-range correlations, while integer-order chaotic systems are generally viewed as a special case of fractional-order counterparts. This close relationship often renders the two difficult to distinguish in practice. However, existing studies mostly design analytical methods for integer-order or fractional-order chaotic systems separately, lacking a unified classification framework that does not rely on prior assumptions about the system order. In this paper, we propose a multi-branch deep learning model integrating a multi-scale convolutional neural network, time–frequency analysis, Transformer blocks, and dynamic memory network to classify integer-order chaos, fractional-order chaos, and steady states. Experiments are conducted on time series from canonical chaotic systems—including the Lorenz, Rössler, Lü, and Chen systems—in both integer- and fractional-order formulations, under two data generation protocols: varying initial conditions and varying system parameters. We evaluate the model under two scenarios: (1) assessing baseline classification performance on noise-free data and (2) testing robustness against increasing levels of Gaussian, salt-and-pepper and Rayleigh noise. The model achieves classification accuracy above 99% on noise-free data across all tested systems. Under noise interference, it demonstrates strong robustness: accuracy remains above 89.7% under high-intensity Gaussian noise. Moreover, we demonstrate that the model trained with fixed system parameters but varying initial conditions generalizes poorly to unseen parameter settings, whereas training with diverse system parameters—while fixing initial conditions—markedly improves generalization. This work offers a data-driven framework for distinguishing integer- and fractional-order chaos and highlights the critical role of training data diversity in building generalizable classifiers for dynamical systems.