Intelligent exogenous networks with Bayesian distributed backpropagation for nonlinear single delay brain electrical activity rhythms in Parkinson's disease system

Abstract

In this study, a novel intelligent adaptive exogenous network backpropagated with a Bayesian distributive scheme is introduced for nonlinear Parkinson's disease systems (NPDS) represented with three differential classes governing the brain's electrical activity rhythms (BEAR) at different cerebral cortex positions considering single and multiple delays in one continuing response. The computing structure is formulated with a multi-layer architecture of nonlinear autoregressive exogenous networks (NARX) with backpropagation through a Bayesian distributed algorithm (BDA). The synthetic datasets for the execution of NARX-BDA are acquired through the Adams numerical solver for NPDS involving single and multiple delays in one variable of BEAR for different sensor locations on the cerebral cortex. The designed computing structure of NARX-BDA is operated arbitrarily for acquired datasets and used for training samples for network formulation on mean square error (MSE) sense while testing samples to validate the performance on unbiased inputs. The exhaustive numerical experimentation studies are conducted for NARX-BDA in solving delayed variants of NPDS, and comparative studies are carried out through numerical solutions by means of convergence curves on MSE for training and testing instances, absolute error, error histograms, statistical studies on regression and correlation measurements to certify the performance.