On Spiking Models for Synaptic Activity and Impulsive Differential Equations | Zendy

Anne Catllá | Zendy; David G. Schaeffer | Zendy; Thomas P. Witelski | Zendy; Eric Monson | Zendy; Anna L. Lin | Zendy

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On Spiking Models for Synaptic Activity and Impulsive Differential Equations

Author(s) -

Anne Catllá,

David G. Schaeffer,

Thomas P. Witelski,

Eric Monson,

Anna L. Lin

Publication year - 2008

Publication title -

siam review

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 4.683

H-Index - 120

eISSN - 1095-7200

pISSN - 0036-1445

DOI - 10.1137/060667980

Subject(s) - limiting , forcing (mathematics) , mathematics , differential equation , interpretation (philosophy) , state (computer science) , computer science , mathematical analysis , algorithm , mechanical engineering , engineering , programming language

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.

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