(636b) Coarse-Grained Dynamics Of A Neural Field Model

We study a stochastic spatio-temporal pattern forming system used to model neural activity in the cortex. Neural dynamics are intrinsically noisy, and we investigate the effects of noise on models for pattern formation. In the absence of noise the system dynamics display a single stable activity ?bump? that moves around the (periodic) domain in one direction; in the presence of noise the bump occasionally switches direction.

We derive an effective low-dimensional description of the system by data processing (using diffusion maps) the results of short bursts of direct simulation. We utilize this reduced representation, in the form of an effective Langevin equation characterized by a double-well potential, and illustrate that it is quantitatively accurate. This approach bypasses the difficult task of deriving such a potential from the original high-dimensional, stochastic system. Computational bifurcation analysis is also presented based on the coarse-grained description of the system. The noisy discretized system is shown to undergo an effective pitchfork bifurcation. The effective potential and the effects of changing parameters on this potential are also studied.

Finding a low-dimensional description for this system not only enhances our insight into the fundamental dynamics, but also enables us to simulate and analyze this system in a computationally expedient manner. We expect such an approach to be widely applicable to other complex systems.