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Coarse-grained dynamics of an activity bump in a neural field model

C. R. Laing·T. A. Frewen·I. G. Kevrekidis
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Abstract

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.

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C. R. Laing, T. A. Frewen, I. G. Kevrekidis. 2006-12-20. Coarse-grained dynamics of an activity bump in a neural field model. https://doi.org/10.1088/0951-7715%2F20%2F9%2F007

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