Compact dynamical model of brain activity

A compact physiologically based mean-field formulation of brain dynamics is proposed to model observed brain activity and electroencephalographic (EEG) signals. In contrast to existing formulations, which are more detailed and complicated, our model is described by a single second-order delay differential equation that encapsulates salient aspects of the physiology. The model captures essential features of activity mediated by fast corticocortical connections and delayed feedbacks via extracortical pathways and external stimuli. In the linear regime, these features can be simply expressed by three coefficients derived from the properties of these physiological pathways and explicit nonlinear approximations are also derived. This compact model successfully reproduces the main features of experimental EEG's and the predictions of previous models, including resonance peaks in EEG spectra and nonlinear dynamics. As an illustration, key features of the dynamics of epileptic seizures are shown to be reproduced by the model. Due to its compact form, the model will facilitate insight into nonlinear brain dynamics via standard nonlinear techniques and will guide analysis and investigation of more complex models. It is thus a useful tool for analyzing complex brain activity, especially when it exhibits low-dimensional dynamics.