STEADY-STATES AND GLOBAL DYNAMICS OF ELECTRICAL-ACTIVITY IN THE CEREBRAL-CORTEX

Steady states and global dynamics of electrical activity in the cerebr al cortex are investigated within the framework of a recent continuum model. It is shown that for a particular physiologically realistic cla ss of models, at most three steady states can occur, two of which are stable. The global dynamics of spatially uniform activity states is st udied and it is shown that in a physiologically realistic class of mod els, 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 deriv e a simplified dynamical equation in the friction-dominated limit. Sol utions of these equations are compared with those of the full global d ynamics equations and it is found that they are adequate for time scal es longer than approximately 100 ms provided dendritic integration tim es are less than approximately 10 ms.