,
Collar A.F.
Faculty Of Physics And Mathematics, Benemerita Universidad Autonoma De Puebla, Mexico E-mail:fraguela@fcfm.buap.mx
This work study models that permit to describe the temporal and spatial dynamic of the actives cortical sources and permit to relate the synaptic activity with the measures potential in EEG.
For the local interaction of a neuronal mass of the cerebral cortex
in a unidimensional model; we get the following system of equations:
,
where 
is the density of
synaptic activity (+ excitatory, inhibitory ) in the column of cortex centered
in the point x in a instant t, this mean, the number of active
synapsis by square centimeter on x,. in the time t; 
is
the total fraction of neurons on the column x that "shoot"
in the time t, 
is the
number of synaptic connections by square centimeter on x provided by a
unit of length of neurons in x, and 
is the density of synaptic activity on the column x in the time
t produced for the external entrance to the cortex. In this model
the function g is a sigmoid function of the variables 
and 
this mean, 
,
if 
and 
if
, where 
,
, 
,
are certain constants and g
is a real function of the variables 
with values [0,1]. In the exposition we will talk about the deduction of
this model and the problem of the existence of rhythms. Also we will talk
about other more complicated models where the scale of decreasing 
for the synaptic connections is constant only locally.