Panic disorder is a debilitating disease that has been reported to have a lifetime prevalence of about 4% and has been recurrently linked with the instance of other mental disorders, such as depression with which it has reportedly significant comorbidity. However, there have been a number of reports about the current state of underdiagnoses of panic disorder, because of its largely prominent somatic symptoms, which cause afflicted individuals to seek clinical care as opposed to mental health consultation and treatments. This study aimed to explore the plausibility of creating an EEG-based machine learning classifier that could serve as a diagnostic aid for panic disorder and address the underdiagnoses. In addition to this, by applying a non-linear dynamical analysis procedure towards studying the effects of panic disorder on the brain using the method of chaos-wavelets that allows insights into the changes in each EEG sub-band, this study aims to show insights to panic disorder using techniques that have largely not been used to explore panic disorder in the brain. The results from this study showed an SVM based classifier for Panic vs. Depression with 86% classification accuracy and a KNN based classifier for panic vs Controls with 76% Classification accuracy. Differences in Approximate entropy between panic disorder and MDD patients were also observed along with Potential channel asymmetry differences in the correlation dimension after Bonferroni correction, between panic disorder patients and the control group.