Steady states and global dynamics of electrical activity in the cerebral cortex

Steady states and global dynamics of electrical activity in the cerebral cortex are investigated within the framework of a recent continuum model. It is shown that for a particular physiologically realistic class of models, at most three steady states can occur, two of which are stable. The global dynamics of spatially uniform activity states is studied and it is shown that in a physiologically realistic class of models, the adiabatic dynamics is governed by a second-order differential equation equivalent to that for the motion of a Newtonian particle in a potential in the presence of friction. This result is used to derive a simplified dynamical equation in the friction-dominated limit. Solutions of these equations are compared with those of the full global dynamics equations and it is found that they are adequate for time scales longer than approximately 100 ms provided dendritic integration times are less than approximately 10 ms.