Attractors
If a RBN
evolves according to one of the update schemes described in Classification,
sooner or later the network gets trapped in an attractor. An
attractor is defined as a sequence of nodestates that the network
repeatedly visits.
In practice, the sequence of nodestates in an attractor and
the length of this sequence, the attractor length, are of
particular interest. An attractor can either be a point attractor
or a cycle attractor, where point attractors have  by definition
attractor length one. Not all update modes exhibit both types of
attractors (ARBN for example do not have cycle attractors due to
the asynchronicity of their update scheme).
Depending on the initial state, a network evolves into the
direction of a specific attractor.
All possible nodestates and the attractors of a network can be
represented by a landscape and described by the notion of
stability/instability. A ball that is placed in a landscape with
hills and valleys, will finally (due to gravity) end up at the
bottom of a valley, which is a stable position in the system. A
network does similarly: it develops through node states
(descending the hills) into an attractor (bottom of the valley).
All nodestates that lead to a specific attractor are said to be
in the basin of attraction of this attractor. Attractors are
interesting because they represent the total number of alternative
and stable longterm behaviours of the system. It might be
interesting to study, how minimal changes in the topology
(connections, nodestates, rules) affect the location and size of
an attractor.
