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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 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)
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 analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front(More)
A mathematical theory of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the anisotropic nature of long-range lateral connections. Each hypercolumn is modeled as a ring of interacting excitatory and inhibitory neural populations with orientation preferences over the range 0 to 180 degrees. Analytical(More)
We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the(More)
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞ , where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking(More)
A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which(More)
We analyze the existence and stability of stimulus-locked traveling waves in a one-dimensional synaptically coupled excitatory neural network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output firing rate of a neuron is taken to be(More)