Nonlocal Ginzburg-Landau equation for cortical pattern formation
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Published version
Author(s)
Bressloff, Paul C
Kilpatrick, Zachary P
Type
Journal Article
Abstract
We show how a nonlocal version of the real Ginzburg-Landau (GL) equation arises in a large-scale recurrent network model of primary visual cortex. We treat cortex as a continuous two-dimensional sheet of cells that signal both the position and orientation of a local visual stimulus. The recurrent circuitry is decomposed into a local part, which contributes primarily to the orientation tuning properties of the cells, and a long-range part that introduces spatial correlations. We assume that (a) the local network exists in a balanced state such that it operates close to a point of instability and (b) the long-range connections are weak and scale with the bifurcation parameter of the dynamical instability generated by the local circuitry. Carrying out a perturbation expansion with respect to the long-range coupling strength then generates a nonlocal coupling term in the GL amplitude equation. We use the nonlocal GL equation to analyze how axonal propagation delays arising from the slow conduction velocities of the long-range connections affect spontaneous pattern formation.
Date Issued
2008-10
Date Acceptance
2008-10-01
Citation
Physical Review E, 2008, 78 (4)
ISSN
1539-3755
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
78
Issue
4
Copyright Statement
©2008 American Physical Society
Identifier
http://dx.doi.org/10.1103/physreve.78.041916
Publication Status
Published
Article Number
041916
Date Publish Online
2008-10-24