Epilepsy is a long-lasting neurological issue characterized by standard, recurrent inflammatory attacks of abnormal brain activity. Its diagnosis is crucial but relies on excruciatingly long electroencephalogram (EEG) readings that are interpreted by medical professionals, which is tedious and time-consuming. In order to address these issues, this proposed study will explore the possibility of detecting epileptic activity in an EEG signal through the use of a freely accessible, open-source database by applying an automated epilepsy detection method. The method of analysis involves nonlinear chaotic properties that are naturally dynamic and complex in brain activity. Specifically, there are four significant characteristics that are computed, and they include the Largest Lyapunov Exponent, Hurst Exponent, Recurrence Quantification Analysis (RQA) measures, and Fractal Dimension. A support vector machine (SVM) classifier is then applied to the features because it can operate well on high-dimensional and nonlinear data. Its success was challenged with five distinct categories of EEG data, whose average classification accuracy was very high at 98.9%. The results prove the great potential of the suggested system as an effective and reliable tool for detecting a disease as epilepsy that offers both speed and precision in clinical and research activities.