Brain electro- (EEG) or magnetoencephalogram (MEG) can be analyzed by using methods of the nonlinear system theory. We show that even for very short and nonstationary time series it is possible to functionally differentiate various brain activities. Usually the analysis assumes that the analyzed signals are both long and stationary, so that the classic spectral methods can be used. Even more convincing results can be obtained under these circumstances when the dimensional analysis or estimation of the Kolmogorov entropy or the Lyapunov exponent are performed. When measuring the spontaneous activity of a human brain the assumption of stationarity is questionable and `static' methods (correlation dimension, entropy, etc.) are then not adequate. In this case `dynamic' methods like pointwise-D2 dimension or chaoticity measures should be applied. Predictability measures in the form of local Lyapunov exponents are capable of revealing directly the chaoticity of a given process, and can practically be applied for functional differentiation of brain activity. We exemplify these in cases of apallic syndrome, tinnitus and schizophrenia. We show that: the average chaoticity in apallic syndrome differentiates brain states both in space and time, chaoticity changes temporally in case of schizophrenia (critical jumps of chaoticity), chaoticity changes locally in space, i.e., in the cortex plane in case of tinnitus.