We analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any noise, the system supports spontaneously propagating traveling pulses that can lock to externally moving stimuli. Using a separation of time-scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the wave from its uniformly translating position at long time-scales, and fluctuations in the wave profile around its instantaneous position at short time-scales. In the case of freely propagating pulses, the wandering is characterized by pure Brownian motion, whereas in the case of stimulus-locked pulses, it is given by an Ornstein-Uhlenbeck process. This establishes that stimulus-locked pulses are more robust to noise.
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 30 October 2012.
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