The importance of understanding the nonlinear
dynamics of neural systems, and the relation
to cognitive systems more generally, has
been recognized for a long time. Approaches
that analyse neural systems in terms of attractors
of autonomous networks can be successful
in explaining system behaviours in
the input-free case. ...
The importance of understanding the nonlinear
dynamics of neural systems, and the relation
to cognitive systems more generally, has
been recognized for a long time. Approaches
that analyse neural systems in terms of attractors
of autonomous networks can be successful
in explaining system behaviours in
the input-free case. Nonetheless, a computational
system usually needs inputs from its
environment to effectively solve problems, and
this necessitates a non-autonomous framework
where typically the effects of a changing
environment can be studied. In this review
we highlight a variety of network attractors
that can exist in autonomous systems
and can be used to aid interpretation of the
dynamics in the presence of inputs. Such
network attractors (that consist of heteroclinic
or excitable connections between invariant
sets) lend themselves to modelling discretestate
computations with continuous inputs,
and can sometimes be thought of as a hybrid
model between classical discrete computation
and continuous-time dynamical systems.