This paper proposes a new method for analyzing brain activity from Electroencephalogram (EEG) based on a concept of instantaneous equivalent bandwidths (IEBWs). The essence of the method using the IEBW is to track bandwidths changes of EEG signals. The instantaneous equivalent bandwidths are defined using positive time-frequency distributions. However, it is well known that non-negative bilinear distributions that satisfy the marginals do not exist. To solve the problem, Copula-based time-frequency distributions have been adopted and we have also modified the construction method suitable for non-stationary random signals. The method was applied to EEG analysis in the wakefulness maintenance state against sleepiness. In our present study, sporadic synchronization was shown in the EEG signals while the subjects were trying to maintain wakefulness against sleepiness. That is, synchronization and desynchronization seem to succeed each other in the period. The results imply that the proposed method can track the EBWs change of EEG signals.