Multiresolution wavelet analysis of transients: numerical simulations and application to EEG

We explore the capabilities of multiresolution wavelet analysis (MWA) to characterize complex dynamics based on short data sets that can be applied for diagnosing inter-state transitions. Using the example of chaos–hyperchaos transitions in the model of two interacting Rössler systems, we establish the minimum amount of data necessary for reliable separation of chaotic and hyperchaotic oscillations and discuss how this amount changes depending on the length of the transient process. We then discuss transitions between wakefulness and artificial sleep in mice and estimate the duration of electroencephalograms (EEG) that provide separation between these states.