Nonlinear dynamics has recently been extensively used to study epilepsy due to the complex nature of the neuronal systems. This study presents a novel method that characterizes the dynamic behavior of pediatric seizure events and introduces a systematic approach to locate the nullclines on the phase space when the governing differential equations are unknown. Nullclines represent the locus of points in the solution space where the components of the velocity vectors are zero. A simulation study over 5 benchmark nonlinear systems with well-known differential equations in three-dimensional exhibits the characterization efficiency and accuracy of the proposed approach that is solely based on the reconstructed solution trajectory. Due to their unique characteristics in the nonlinear dynamics of epilepsy, discriminative features can be extracted based on the nullclines concept. Using a limited training data (only 25% of each EEG record) in order to mimic the real-world clinical practice, the proposed approach achieves 91.15% average sensitivity and 95.16% average specificity over the benchmark CHB-MIT dataset. Together with an elegant computational efficiency, the proposed approach can, therefore, be an automatic and reliable solution for patient-specific seizure detection in long EEG recordings.