Nonlinear dynamical systems exhibit a wide variety of dynamic behaviour, including chaotic dynamics. Previous studies have reported the chaotic nature of EEG (Electroencephalogram) signals and various feature extraction techniques for pattern recognition. This work is an effort to investigate the complex underlying dynamics of chaotic systems and to develop a machine learning based pattern recognition and feature extraction of EEG signals for computer aided diagnosis of depression. Chaotic systems which are designed by known equations can be easily controlled and is possible to predict future values, on the other hand, EEG signals are prone to noise and the available data is limited. To this end, this thesis first develops a novel extension of ANN(Artificial Neural Networks) based modelling for chaotic systems. The Rossler’s and Chua’s systems are used for the study. A NARX (Nonlinear Autoregressive Exogenous) model is proposed to train bifurcation patterns of chaotic systems and performance of various NARX topologies in modelling the bifurcation patterns is estimated. Previous efforts to model an attractor were based on open loop ANN models, a feedback ANN model is proposed by the author to evaluate the modelling performance. MLP (Multilayer Perceptron) and RBFN (Radial Basis Function Network) are studied and employed to model an attractor and a comparison of the MSE(Mean Squared Error) performance between two systems based on the computational cost is done. The dynamic invariants of the modelled signals are estimated and compared with the output of the original signals. Finally, a qualitative study of the modelling system is generated, which includes superposition of model on top of original output plots and calculating the model run time. The second part of the thesis talks about pattern recognition and classification of EEG signals of depression subjects from healthy controls based on chaotic systems. Temporal features and temporal-spectral features are extracted from the EEG data collected from subjects suffering from depression, a psychiatric neural disorder collected and a comparison of the pattern recognition performance is done. The pattern recognition of chaotic systems: Lorenz, Rossler and Chen systems is formulated into a two-class classification task and evaluated first. Both statistical and ANN based classifiers such as Decision tree, K-NN(K-Nearest Neighbor), SVM(Support Vector Machine), MLP and kfold cross validation of MLP are used for the study. . Insomnia and narcolepsy are the two main depression symptoms shown by subjects and data are collected from publicly available databases. Diagnosing depression in the early curable stage is very important. The computer aided depression diagnosis uses machine learning classifiers to recognize EEG data of people showing depression symptoms and classifies it from the control set. . The results are compared with previous studies and found to be superior in terms of performance and complexity of the techniques used.