Nonlinear dynamic system theory offers fresh perspectives on how to analyse and comprehend intricate structures. It provides novel ideas, algorithms, and techniques for signal processing, analysis, and categorization. Now, scientists are using these ideas to investigate the dynamics of physiological signals. Nonlinear dynamics theory is applied to electroencephalogram (EEG) signals in this work to better comprehend emotional and cognitive states. In this thesis, three distinct mental disorders; epilepsy, alcoholism, and depression are examined. Due to the unpredictable nature of epileptic seizures, the illness is notoriously challenging to diagnose and treat. Patients and their loved ones would benefit greatly from an automated approach that defines epileptic activity in EEG signals. Therefore, critical clinical information can be revealed and the condition can be better managed. Feature extraction, as well as the creation and testing of classifiers, were performed on the EEG data that belonged to the various categories. Wavelet packet decomposition (WPD) is applied to the EEG signals. Different parts of the WPD are used to isolate the HOS cumulants. The HOS cumulants are analysed using an ANOVA test for significant characteristics (p < 0.05). These traits are then used as inputs to various classifiers to facilitate automatic classification. Using this method, we are able to reliably categorise EEG signals into three distinct types with a precision of 98%.