Towards a comprehensive theory of brain activity:: Coupled oscillator systems under external forces

Recently, Jirsa et al. and Haken discussed a theory comprising the brain wave equation proposed by Nunez, the Wilson–Cowan/Ermentrout–Cowan model, and Hopfield networks. This theory was applied to model findings obtained in an experiment that relates brain activity and behavior, the so-called Julliard experiment. In previous works of Jirsa et al. and Frank et al. the focus was on the brain wave aspect. Recently, we conducted similar experiments. The results obtained are modeled in this paper in terms of coupled oscillator systems. Coupled oscillator systems are considered to represent the Wilson–Cowan/Ermentrout–Cowan-model aspect of the unifying theory. Building on a model proposed by Haken, Kelso, and Bunz and the theory of weakly coupled oscillators established by Winfree and by Kuramoto, we derive a nonlinear Fokker–Planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments.