Mathematics – Dynamical Systems
Scientific paper
2006-12-20
Mathematics
Dynamical Systems
Corrected aknowledgements
Scientific paper
10.1088/0951-7715/20/9/007
We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar "coarse" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based "intelligent" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach.
Frewen Thomas A.
Kevrekidis Ioannis G.
Laing Carlo R.
No associations
LandOfFree
Coarse-grained dynamics of an activity bump in a neural field model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Coarse-grained dynamics of an activity bump in a neural field model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coarse-grained dynamics of an activity bump in a neural field model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-22441