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 wa ve equation proposed by Nunez, the Wilson-Cowan/Ermentrout-Cowan model, and Hopfield networks. This theory was applied to model findings obtained in a n experiment that relates brain activity and behavior, the so-called Jullia rd 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 oscillat or systems. Coupled oscillator systems are considered to represent the Wils on-Cowan/Ermentrout-Cowan-model aspect of the unifying theory. Building on a model proposed by Haken, Kelso, and Bunt 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 bra in activity observed in our experiments. (C) 2000 Elsevier Science B.V. All rights reserved.