Modeling and Complexity Analysis of Fuzzy-Fractional Chaotic Systems Using Deep Neural Networks

Nonlinear dynamical systems exhibiting chaos, memory and uncertainty effects play a vital role in the modeling of complex phenomena in science and engineering. Due to the rapid growing of development in machine learning and artificial intelligence, data-driven methods have been widely used for predicting and analysing nonlinear dynamical systems. Neural network-based architectures have demonstrated strong potential in learning hidden dynamics directly from time-series data. In this study, a data-driven framework is proposed for modeling and analysis of fuzzy-fractional chaotic systems with special focus on Lorenz, Chen, and Burke–Shaw type models. Uncertainty and imprecision in system parameters are incorporated through triangular fuzzy numbers, leading to fuzzy-fractional formulations capable of capturing richer dynamical behaviours. Time-series trajectories are initially generated using an explicit fractional-order Runge–Kutta scheme and subsequently employed to train an autoregressive residual multilayer perceptron to learn the underlying system evolution directly from data. The proposed learning architecture effectively produces long-term dynamics of considered systems. To quantify the performance of the proposed residual multilayer perceptron, a comprehensive dynamical analysis is conducted through computation of the full Lyapunov spectrum and Kaplan–Yorke dimension, providing insights into sensitivity to initial conditions, attractor dimensionality, and emergent chaotic behaviour. The results demonstrate that proposed framework offers a robust and scalable approach for capturing, analyzing, and quantifying complexity in fuzzy-fractional chaotic systems, thereby contributing to the understanding of uncertainty-driven dynamics in nonlinear complex systems. Notably, hyperchaotic behaviour characterised by two positive Lyapunov exponents is detected in the fuzzy-fractional Chen system under six out of nine parameter configurations. In fuzzy-fractional Burke–Shaw system, hyperchaos is also observed for some combinations of fractional-order and fuzzy cut level.