In this paper, the performance of the phase space representation in interpreting the underlying dynamics of epileptic seizures is investigated and a novel patient-specific seizure detection approach is proposed based on the dynamics of EEG signals. To accomplish this, the trajectories of seizure and nonseizure segments are reconstructed in a high dimensional space using time-delay embedding method. Afterwards, Principal Component Analysis (PCA) was used in order to reduce the dimension of the reconstructed phase spaces. The geometry of the trajectories in the lower dimensions is then characterized using Poincaré section and seven features were extracted from the obtained intersection sequence. Once the features are formed, they are fed into a two-layer classification scheme, comprising the Linear Discriminant Analysis (LDA) and Naive Bayesian classifiers. The performance of the proposed method is then evaluated over the CHB-MIT benchmark database and the proposed approach achieved 88.27% sensitivity and 93.21% specificity on average with 25% training data. Finally, we perform comparative performance evaluations against the state-of-the-art methods in this domain which demonstrate the superiority of the proposed method.