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On Spiking Models for Synaptic Activity and Impulsive Differential Equations

SIAM Rev. Volume 50, Issue 3, pp. 553-569 (2008)

Published August 5, 2008
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We illustrate the problems that can arise in writing differential equations that include Dirac delta functions to model equations with state-dependent impulsive forcing. Specifically, difficulties arise in the interpretation of the products of distributions with discontinuous functions. We suggest several methods to resolve these ambiguities, such as using limiting sequences and asymptotic analysis, with applications of the results given for discrete maps. These suggestions are applied to a popular model describing synaptic connections in the brain.

©2008 Society for Industrial and Applied Mathematics
History: Received August 22, 2006; accepted July 11, 2007; published August 5, 2008
Permalink: http://dx.doi.org/10.1137/060667980

KEYWORDS and AMS

Keywords
AMS Subject Classifications
34K45, 24K26, 34E10

PUBLICATION DATA

ISSN:
0036-1445 (print)   1095-7200 (online)
Publisher:
AIP is a member of CrossRef SIAM

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