Characteristics of neuronal systems in the visual cortex
Biological Cybernetics
Controlling the Speed of Synfire Chains
ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks
Neural Field Model of Receptive Field Restructuring in Primary Visual Cortex
Neural Computation
Nonlinear Analysis of Simple Cell Tuning in Visual Cortex
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
A new clustering approach on the basis of dynamical neural field
Neural Computation
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This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called "bumps") in non-linear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady-state receptive fields and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural fields. Full spatiotemporal response profiles can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural field models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations.