This thesis addresses some theoretical issues generated by the results of recent analysis of EEG time series proving the brain dynamics are driven by abrupt changes making them depart from the ordinary Poisson condition. These changes are renewal, unpredictable and non-ergodic. We refer to them as crucial events. How is it possible that this form of randomness be compatible with the generation of waves, for instance alpha waves, whose observation seems to suggest the opposite view the brain is characterized by surprisingly extended coherence? To shed light into this apparently irretrievable contradiction we propose a model based on a generalized form of Langevin equation under the influence of a periodic stimulus. We assume that there exist two different forms of time, a subjective form compatible with Poisson statistical physical and an objective form that is accessible to experimental observation. The transition from the former to the latter form is determined by the brain dynamics interpreted as emerging from the cooperative interaction among many units that, in the absence of cooperation would generate Poisson fluctuations. We call natural time the brain internal time and we make the assumption that in the natural time representation the time evolution of the EEG variable …