NDLI: Threshold of Front Propagation in Neural Fields: An Interface Dynamics Approach

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Faye, Grégory Kilpatrick, Zachary P.
Copyright Year	2018
Abstract	Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics are more challenging to study, due to the nonlinearity and nonlocality of neural fields, whose interactions are described by the kernel of an integral term. Here, we leverage interface methods to describe the threshold of wave initiation away from equilibrium. In particular, we focus on traveling front initiation in an excitatory neural field. In a neural field with a Heaviside firing rate, neural activity can be described by the dynamics of the interfaces, where the neural activity is at the firing threshold. This allows us to derive conditions for the portion of the neural field that must be activated for traveling fronts to be initiated. Explicit equations are possible for a single active (superthreshold) region and special cases of multiple disconnected active regions. The dynamic spreading speed of the excited region can also be approximated asymptotically. We also discuss extensions to the problem of finding the critical spatiotemporal input needed to initiate waves.
Sponsorship	Agence Nationale de la Recherche. National Science Foundation
Starting Page	2575
Ending Page	2596
Page Count	22
File Format	PDF
ISSN	00361399
DOI	10.1137/18M1165797
e-ISSN	1095712X
Issue Number	5
Volume Number	78
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-25
Access Restriction	Subscribed
Subject Keyword	interface equations neural field equations traveling fronts propagation threshold Integro-partial differential equations Neural biology
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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