The field operations considered above are examples of nonrecurrent operations, typically implemented by feed-forward connections between neural areas. In this section we will consider recurrent operations, which are typically implemented by feed-back or reciprocal connections. Thus there are dynamical relations between several areas that govern the variation in time of one or more fields; these processes are especially important in motor control, since time-varying motor fields in the central and peripheral nervous systems must be generated to control physical movement.
Field dynamics are most conveniently expressed by
differential field equations, in which the time-derivative 
of a state field 
is given as a function
of the current state field 
and some, possibly
time-varying, input field 
:
[ .(t) = F[ (t), (t) ] . ]
More generally, we may have a system of state fields
, 
, each evolving under the influence
of each other and one or more input fields 
,
.
Thus,
[ _k(t) =
F_k[ _1(t), ...,_m(t);
_1(t),..., _n(t) ] . ]
(For purposes of mathematical modeling, equations involving
second- and higher-order time derivatives can be placed in
this form by adding state fields to explicitly represent
derivatives, in which case we must carefully distinguish
fields represented in neural tissue from those introduced for
mathematical convenience.)
As before, we may distinguish between the cases in which the
dependence is (approximately) linear or not.