Electroencephalography (EEG) signals are inherently non-linear, non-stationary, and vulnerable to noise sources, making the extraction of discriminative features a long-standing challenge. In this work, we investigate the non-linear Teager-Kaiser Energy Operator (TKEO) for modeling the underlying energy dynamics of EEG in three representative tasks: motor imagery, emotion recognition, and epilepsy detection. To accommodate the narrowband nature of the operator, we employ Gabor filterbanks to isolate canonical frequency bands, followed by the Energy Separation Algorithm to decompose the TKEO output into an amplitude envelope and instantaneous frequency components. We then derive a set of energy descriptors based on this demodulation and compare their classification performance against established EEG features. The proposed TKEO-based pipeline offers an intuitive, physiologically grounded framework for capturing EEG signal dynamics, while remaining simple, training-free, and data-efficient. Our findings suggest that combining TKEO features with conventional ones improves Balanced Accuracy by approximately 15 percent in epilepsy detection, yields modest gains in motor imagery, and achieves on par performance in emotion recognition, reflecting the pipeline's ability to capture transient neural dynamics.