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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.
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stab
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external
In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence, that is believed to restore normal dif
In the present paper we describe the properties induced by disorder on an ultracold gas of Bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centered on the spatial d
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per node can