Dynamic Neural Field Theory for Motion Perception
Dynamic Neural Field Theory for Motion Perception
Self-Localization of Autonomous Robots by Hidden Representations
Autonomous Robots
Saccade Control through the Collicular Motor Map: Two-Dimensional Neural Field Model
ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks
Spontaneous symmetry breaking in self–organizing neural fields
Biological Cybernetics
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
Neural Field Model of Receptive Field Restructuring in Primary Visual Cortex
Neural Computation
Traveling bumps and their collisions in a two-dimensional neural field
Neural Computation
| Hi-index | 0.00 |
We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case was treated comprehensively by Amari 30 years ago, two-dimensional neural fields are much less understood. We derive conditions for the stability for the main classes of localized solutions of the neural field equation and study their behavior beyond parameter-controlled destabilization. We show that a slight modification of the original model yields an equation whose stationary states are guaranteed to satisfy the original problem and numerically demonstrate that it admits localized noncircular solutions. Typically, however, only periodic spatial tessellations emerge on destabilization of rotationally invariant solutions.