  We have used a mean-field Monte Carlo method to study the zero-temperature
synchronous dynamics of a one-pattern model of associative memory with random
asymmetric couplings. In the case of symmetric couplings, we find evidence for
a transition from a spin-glass-like phase to a ferromagnet-like phase as the
acquisition strength of the stored pattern is increased from zero. In the
ferromagnetic phase, we find the existence of two types of phase-space
structure for $m > 0$ where $m$ is the overlap of the state of the system with
the stored pattern: a simple phase-space structure where all initial states
with $m > 0$ flow to the attractor corresponding to the stored pattern; and a
complex phase-space structure with many attractors with their basins of
attraction. The presence of random asymmetry in the couplings results in better
retrieval performance of the network by enhancing the size of the basin of
attraction of the stored pattern and by making the recall of memory
significantly faster.
