Dynamic Neural Network Model Predictor for Fractal HyperChaotic Attractors Based on MLMA Algorithm

Abstract

A dynamic neural network model predictor for fractal strange hyperchaotic
attractor based on modified Levenberg-Marquardt algorithm (MLMA) is
proposed in this article. Six nonlinear fractal strange hyperchaotic attractors
are considered, namely: 1). Rössler’s hyperchaotic system, 2). Chua’s
memristor system, 3). Duffing-Van der Pols system, 4). Xu’s hyperchaotic
system, 5). Lorenz’s hyperchaotic system, and 6). Rabinovich-Fabrikant’s
system. Neural network models trained with the MLMA are inferred to
capture the dynamics of the six nonlinear fractal hyperchaotic attractors. The
trained neural network models are validated by: 1). one-step ahead prediction
of the training data, 2). one-step ahead prediction of the validation data, 3).
Five-step ahead prediction., and 4). Akaike’s final prediction error (AFPE)
estimate of the regularized criterion, The results obtained from the study
shows good agreement of the model predictions based on the proposed
MLMA algorithm in terms of much smaller prediction and estimation errors
as well as significant reduction in computation times when compared to the
time taken by the actual mathematical models. The proposed techniques and
algorithms can be adapted and deployed for the modeling and prediction of
highly nonlinear chaotic systems as well as fractal strange and hyperchaotic
attractors in engineering, financial, biological and management systems,
atmospheric astronomical research, medicine, sciences for modeling,
prediction and control.