Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks

In this study, a novel investigation in developing intelligent adaptive Bayesian networks (IABN) is carried out to solve the fractional order Parkinson's disease model (FOPDM) represented with a system of three fractional differential equations reflecting the brain's electrical activity rhythms at different cerebral cortex positions. The IABN are developed by using the competency of the multi-layer architecture of neural networks with backpropagation through Bayesian regularization optimization scheme. The reference dataset for IABN is created through Grunwald-Letnikov fractional derivative-based numerical solver for FOPDM in case of varying sensor locations on the cerebral cortex, as well as, considering different fractional orders in FOPDM. The proposed IABN is applied to the created datasets arbitrarily partitioned into training and testing sets by optimizing the fitness criterion based on mean square error (MSE) metric. The detailed analyses of the proposed IABN through extensive simulations and comparison with the reference numerical solutions of FOPDM in terms of MSE training/testing plots, absolute error, training/testing regression plots, and error histogram results, endorse the worth of the proposed intelligent scheme for different fractional orders.