Assessment of Fractal Synchronization during an Epileptic Seizure

In this paper, we define fractal synchronization (<i>FS</i>) based on the idea of stochastic synchronization and propose a mathematical apparatus for estimating <i>FS</i>. One major advantage of our proposed approach is that fractal synchronization makes it possible to estimate the aggregate strength of the connection on multiple time scales between two projections of the attractor, which are time series with a fractal structure. We believe that one of the promising uses of <i>FS</i> is the assessment of the interdependence of encephalograms. To demonstrate this approach in evaluating the cross-dependence between channels in a network of electroencephalograms, we evaluated the <i>FS</i> of encephalograms during an epileptic seizure. Fractal synchronization demonstrates the presence of desynchronization during an epileptic seizure.