Artificial Neural Network Modelling of Rossler's and Chua's Chaotic Systems

Abstract

This paper presents the detailed analysis of various Artificial Neural Network (ANN) modelling techniques for chaotic systems. Specifically, Rossler's system and Chua's system are selected for this study for their practical applications, and the outputs of these two systems are used for the ANN training. The Nonlinear Auto-Regressive(NAR) modelling is used for chaotic time series prediction. The Nonlinear Auto-Regressive with Exogenous Inputs (NARX) modelling is used for generating chaotic time series outputs with varying system parameters as exogenous inputs. The research results show that ANN performs well in modelling chaotic systems. Rossler's attractor is modelled using Radial Basis Function Network(RBFN) and a comparative study between FeedForward Neural Network(FFNN) and RBFN is done. The result shows that RBFN uses more neurons to achieve similar training performance compared to FFNN. The 3-layer ANN architecture with hidden neurons varying from 1 to 16 is designed and trained using MATLAB NN toolbox. In a fixed-point FPGA implementation perspective, a study on the performance of ANN modelling of chaotic systems is very relevant.