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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)

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)

We show how a one-dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bidi-rectional wave propagation. We analyze the dynamics in a neighborhood of the front… (More)

We use averaging and homogenization theory to study the propagation of traveling pulses in an inhomogeneous excitable 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. We show how a spatially periodic modulation of homogeneous… (More)

- Stefanos E Folias, Shan Yu, Abigail Snyder, Danko Nikolić, Jonathan E Rubin
- The European journal of neuroscience
- 2013

Neurons in the visual cortex exhibit heterogeneity in feature selectivity and the tendency to generate action potentials synchronously with other nearby neurons. By examining visual responses from cat area 17 we found that, during gamma oscillations, there was a positive correlation between each unit's sharpness of orientation tuning, strength of… (More)

- Stefanos E Folias, Danko Nikolić, Jonathan E Rubin
- 2011

Parallel multiunit recordings from V1 in anesthetized cat were collected during the presentation of ran-domÂ sequences of drifting sinusoidal gratings at 12 fixed orientations while gamma oscillations were present. In agreement with the seminal work [1], most units were orientation selective to varying degrees and synchronization was evident in spike trainÂ… (More)

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