High-density electrocorticogram (ECoG) electrodes are capable of recording neurophysiological data with high temporal resolution with wide spatial coverage. These recordings are a window to understanding how the human brain processes information and subsequently behaves in healthy and pathologic states. Here, we describe and implement delay differential analysis (DDA) for the characterization of ECoG data obtained from human patients with intractable epilepsy. DDA is a time-domain analysis framework based on embedding theory in nonlinear dynamics that reveals the nonlinear invariant properties of an unknown dynamical system. The DDA embedding serves as a low-dimensional nonlinear dynamical basis onto which the data are mapped. This greatly reduces the risk of overfitting and improves the method's ability to fit classes of data. Since the basis is built on the dynamical structure of the data, preprocessing of the data (e.g., filtering) is not necessary. We performed a large-scale search for a DDA model that best fit ECoG recordings using a genetic algorithm to qualitatively discriminate between different cortical states and epileptic events for a set of 13 patients. A single DDA model with only three polynomial terms was identified. Singular value decomposition across the feature space of the model revealed both global and local dynamics that could differentiate electrographic and electroclinical seizures and provided insights into highly localized seizure onsets and diffuse seizure terminations. Other common ECoG features such as interictal periods, artifacts, and exogenous stimuli were also analyzed with DDA. This novel framework for signal processing of seizure information demonstrates an ability to reveal unique characteristics of the underlying dynamics of the seizure and may be useful in better understanding, detecting, and maybe even predicting seizures.