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Interface dynamics in planar neural field models

Coombes, S., Schmidt, H. and Bojak, I. (2012) Interface dynamics in planar neural field models. The Journal of Mathematical Neuroscience, 2 (1). 9. ISSN 2190-8567

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To link to this item DOI: 10.1186/2190-8567-2-9

Abstract/Summary

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Item Type:Article
Refereed:Yes
Divisions:Interdisciplinary centres and themes > Centre for Integrative Neuroscience and Neurodynamics (CINN)
No Reading authors. Back catalogue items
ID Code:32499
Additional Information:The full text of this article is freely available via PMC using the link supplied in Related URLs
Publisher:Springer

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