The Mathematical Institute, University of Oxford, Eprints Archive

Front propagation in stochastic neural fields

Bressloff, P. C. and Webber, M. (2011) Front propagation in stochastic neural fields. SIAM Journal on Applied Dynamical Systems . (Submitted)

[img]
Preview
PDF
452Kb

Abstract

We analyse 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 profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein–Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1449
Deposited By:Peter Hudston
Deposited On:18 Nov 2011 07:42
Last Modified:09 Feb 2012 13:49

Repository Staff Only: item control page