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 language||English (US)|
|Number of pages||33|
|Journal||SIAM Journal on Applied Dynamical Systems|
|State||Published - Jan 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
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 KUK-C1-013-04), and the Systems Biology Doctoral Training Centre, University of Oxford. We are also grateful for access to the Oxford Supercomputing Center.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.