  Attractor models are simplified models used to describe the dynamics of
firing rate profiles of a pool of neurons. The firing rate profile, or the
neuronal activity, is thought to carry information. Continuous attractor neural
networks (CANNs) describe the neural processing of continuous information such
as object position, object orientation and direction of object motion.
Recently, it was found that, in one-dimensional CANNs, short-term synaptic
depression can destabilize bump-shaped neuronal attractor activity profiles. In
this paper, we study two-dimensional CANNs with short-term synaptic depression
and with spike frequency adaptation. We found that the dynamics of CANNs with
short-term synaptic depression and CANNs with spike frequency adaptation are
qualitatively similar. We also found that in both kinds of CANNs the
perturbative approach can be used to predict phase diagrams, dynamical
variables and speed of spontaneous motion.
