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

Type
Article

Authors
Webber, Matthew A
Bressloff, Paul C

KAUST Grant Number
KUK-C1-013-04

Date
2013-03-12

Abstract
We analyze 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 extrinsic 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. 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 lead to quenched disorder in the neural fields during propagation of a wave. © 2013 IOP Publishing Ltd and SISSA Medialab srl.

Citation
Webber MA, Bressloff PC (2013) The effects of noise on binocular rivalry waves: a stochastic neural field model. Journal of Statistical Mechanics: Theory and Experiment 2013: P03001. Available: http://dx.doi.org/10.1088/1742-5468/2013/03/p03001.

Acknowledgements
This publication was based on work supported in part by the National Science Foundation (DMS-1120327), the King Abdullah University of Science and Technology Award No. KUK-C1-013-04, and the Systems Biology Doctoral Training Centre, University of Oxford.

Publisher
IOP Publishing

Journal
Journal of Statistical Mechanics: Theory and Experiment

DOI
10.1088/1742-5468/2013/03/p03001

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