Modeling chaotic diabetes systems using fully recurrent neural networks enhanced by fractional-order learning

Modeling nonlinear medical systems plays a vital role in healthcare, especially in understanding complex diseases such as diabetes, which often exhibit nonlinear and chaotic behavior. Artificial neural networks (ANNs) have been widely utilized for system identification due to their powerful function approximation capabilities. This paper presents an approach for accurately modeling chaotic diabetes systems using a Fully Recurrent Neural Network (FRNN) enhanced by a Fractional-Order (FO) learning algorithm. The integration of FO learning improves the network's modeling accuracy and convergence behavior. To ensure stability and adaptive learning, a Lyapunov-based mechanism is employed to derive online learning rates for tuning the model parameters. The proposed approach is applied to simulate the insulin-glucose regulatory system under different pathological conditions, including type 1 diabetes, type 2 diabetes, hyperinsulinemia, and hypoglycemia. Comparative studies are conducted with existing models such as FRNNs trained using gradient descent (FRNN-GD), Deep Feedforward Neural Network (DFNN, Diagonal RNNs with gradient descent (DRNN-GD), and DRNNs with FO learning (DRNN-FO). Simulation results confirm that the proposed FRNN-FO model outperforms these alternatives in terms of accuracy and robustness, making it a promising tool for modeling complex biomedical dynamics.