In this paper, we would like to understand whether the dynamical nonstationarity (ie change of parameter for a dynamical system, with respect to time) could significantly detect transitions between states of the brain from macroscales (ie changes of mental state) down to microscales of processing (dynamical units of processing). We used dynamical nonlinear measures and weak statistical indexes (ie mean and variance) to develop a clustering method to assess the detection of dynamically changing points (ie dynamically nonstationary) in artificial time series against various levels of Gaussian noise. We estimated the decision threshold for micro and macrostate detection based on a sensitivity/specificity and Receiver-Operator Characteristics (ROC) and Area Under the Curve (AUC) analysis. We found that the dynamical analysis was better able to discriminate dynamical changing points (AUC> 0.7) than the weak statistical measures (AUC< 0.6) for Gaussian noise of up to 70%. After the validation of the robustness of the dynamical methods against noise, we applied the dynamical nonstationarity analysis to the detection of mental state transition in EEGs of 9 healthy, age-matched subjects performing different mental tasks including resting with eyes opened, a mental calculation and a mental rotation of 3D objects. The dynamical nonstationarity did not show convincing performance for the macroscopic segmentation of the EEG. The characterization of the mental states, however, using the average duration of dynamical stationarity of the associated EEG epochs did point significant differences between mental states and agreed with previous studies. We propose that the mean duration of dynamical stationarity might reflect cognitive mental states. We are planning in applying this characterization of EEG time series for the diagnosis of disorders related to unstable mental state, such as Attention deficit disorders.