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Modeling electrocortical activity through improved local approximations of integral neural field equations

Coombes, S.; Venkov, Nikola; Shiau, LieJune; Bojak, Ingo; Liley, David; Laing, Carlo


Nikola Venkov

LieJune Shiau

Ingo Bojak

David Liley

Carlo Laing


Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat "patchy" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice- directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. © 2007 The American Physical Society.


Coombes, S., Venkov, N., Shiau, L., Bojak, I., Liley, D., & Laing, C. (2007). Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76(5),

Journal Article Type Article
Acceptance Date Jun 27, 2007
Publication Date Nov 1, 2007
Deposit Date Oct 3, 2007
Publicly Available Date Nov 1, 2007
Journal Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 76
Issue 5
Keywords neural fields, brain wave equations, patchy connections
Public URL
Publisher URL
Additional Information Open Access Journal version at:


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