Front Propagation in Stochastic Neural Fields

Paul C. Bressloff, Matthew A. Webber

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

We analyze 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. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)708-740
Number of pages33
JournalSIAM Journal on Applied Dynamical Systems
Volume11
Issue number2
DOIs
StatePublished - Jan 2012
Externally publishedYes

Fingerprint

Dive into the research topics of 'Front Propagation in Stochastic Neural Fields'. Together they form a unique fingerprint.

Cite this