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.
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