We study the notion of a strong attractor of
a Hopfield neural model as a pattern that has been stored
multiple times in the network, and examine its properties
using basic mathematical techniques as well as a variety of
simulations. It is proposed that strong attractors can be used
to model attachment types in developmental psychology as well
as behavioural patterns in psychology and psychotherapy. We
study the stability and basins of attraction of strong attractors
in the presence of other simple attractors and show that they are
indeed more stable with a larger basin of attraction compared
with simple attractors. We also show that the perturbation
of a strong attractor by random noise results in a cluster of
attractors near the original strong attractor measured by the
Hamming distance. We investigate the stability and basins of
attraction of such clusters as the noise increases and establish
that the unfolding of the strong attractor, leading to its break-
up, goes through three different stages. Finally the relation
between strong attractors of different multiplicity and their
influence on each other are studied and we show how the impact
of a strong attractor can be replaced with that of a new strong
attractor. This retraining of the network is proposed as a model
of how attachment types and behavioural patterns can undergo
change.