Wavelet Neural Networks and their application in the study of dynamical systems

Abstract

The main aim of this dissertation is to study the topic of wavelet neural networks and see how they are useful for dynamical systems applications such as predicting chaotic time series and nonlinear noise reduction. To do this, the theory of wavelets has been studied in the first chapter, with the emphasis being on discrete wavelets. The theory of neural networks and its current applications in the modelling of dynamical systems has been shown in the second chapter. This provides sufficient background theory to be able to model and study wavelet neural networks. In the final chapter a wavelet neural network is implemented and shown to accurately estimate the dynamics of a chaotic system, enabling prediction and enhancing methods already available in nonlinear noise reduction.