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Progress during the past decade in non-linear dynamics and instability theory has provided useful tools for understanding spatio-temporal pattern formation. Procedures which apply principle component analysis (using the Karhunen–Loeve decomposition technique) to the multichannel electroencephalograph (EEG) time series have been developed. This technique shows localized changes of cortical functioning; it identifies increases and decreases of the activity of localized cortical regions over time while the subject performs a simple task or test. It can be used to demonstrate the change in cortical dynamics in response to a continuous challenge. Using 16 EEG electrodes, the technique provides spatio-temporal information not obtained with power spectrum analysis, and includes the weighted information given with omega complexity. As an application, we performed a pattern analysis of sleep-deprived human EEG data in 20 healthy young men. Electroencephalograph recordings were performed on subjects for <2 min, with eyes closed after normal sleep and after 24 h of experimentally-induced sleep deprivation. The significant changes in the eigenvector components indicated the relative changes of local activity in the brain with progressive sleep deprivation. A sleep deprivation effect was observed, which was hemispherically correlated but with opposite directional dynamics. These changes were seen in the temporo-parietal regions bilaterally. The application of the technique showed that the simple test task was performed with a limited unilateral hemispheric involvement at baseline, but needed a much larger cortical participation with decreased frontal activity and increased coherence and bilateral hemispheric involvement. The calculations performed demonstrated that the same weighted changes as those obtained with omega complexity were shown, but the technique had the added advantage of showing the localized directional changes of the principle eigenvector at each studied electrode, pointing out the cortical localized region affected by the sleep deprivation and toward which direction the environmental challenge induced the spatial change. This methodology may allow the evaluation of changes in local dynamics in brain activity in normal and pathological conditions.