The Mathematical Institute, University of Oxford, Eprints Archive

The effects of noise on binocular rivalry waves: a stochastic neural field model

Webber, M. and Bressloff, P. C. (2012) The effects of noise on binocular rivalry waves: a stochastic neural field model. Journal of Statistical Mechanics . (Submitted)

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Abstract

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1547
Deposited By:Peter Hudston
Deposited On:05 Jul 2012 08:52
Last Modified:05 Jul 2012 08:52

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