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We survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields. Neural fields model the large-scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial distribution of neuronal synaptic connections.(More)
A central question in visual neuroscience is what circuits generate the responses of neurons in the primary visual cortex (V1). V1 neurons respond best to oriented stimuli of optimal size within their receptive field (RF) center. This size tuning is contrast dependent, i.e. a neuron's optimal stimulus size measured at high contrast (the high-contrast(More)
The responses of neurons in sensory cortices are affected by the spatial context within which stimuli are embedded. In the primary visual cortex (V1), orientation-selective responses to stimuli in the receptive field (RF) center are suppressed by similarly oriented stimuli in the RF surround. Surround suppression, a likely neural correlate of perceptual(More)
We use averaging and homogenization theory to study the propagation of trav-eling wavefronts in an inhomogeneous excitable neural medium. Motivated by the functional architecture of primary visual cortex, we model the inhomogeneity as a periodic modulation in the long-range neuronal connections. We derive an expression for the effective wavespeed and show(More)
This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants comprising (i) gratings, lattices, fretworks, filigrees, honeycombs and chequer-boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv)(More)
In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse solution in an excitatory neural network. A subsequent reduction of the input amplitude can then induce a Hopf instability of the stationary solution resulting in the formation of a breather. The breather can itself undergo a secondary instability leading to the periodic(More)
In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could(More)
In this review we re-examine the concept of a cortical column in macaque primary visual cortex, and consider to what extent a functionally defined column reflects any sort of anatomical entity that subdivides cortical territory. Functional studies have shown that columns relating to different response properties are mapped in cortex at different spatial(More)
In primary visual cortex (V1), neuronal responses to optimally oriented stimuli in the receptive field (RF) center are usually suppressed by iso-oriented stimuli in the RF surround. The mechanisms and pathways giving rise to surround modulation, a possible neural correlate of perceptual figure-ground segregation, are not yet identified. We previously(More)