On spiking models for synaptic activity and impulsive differential equations
Publication
, Journal Article
Catllá, AJ; Schaeffer, DG; Witelski, TP; Monson, EE; Lin, AL
Published in: SIAM Review
September 1, 2008
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.
Duke Scholars
Published In
SIAM Review
DOI
ISSN
0036-1445
Publication Date
September 1, 2008
Volume
50
Issue
3
Start / End Page
553 / 569
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Catllá, A. J., Schaeffer, D. G., Witelski, T. P., Monson, E. E., & Lin, A. L. (2008). On spiking models for synaptic activity and impulsive differential equations. SIAM Review, 50(3), 553–569. https://doi.org/10.1137/060667980
Catllá, A. J., D. G. Schaeffer, T. P. Witelski, E. E. Monson, and A. L. Lin. “On spiking models for synaptic activity and impulsive differential equations.” SIAM Review 50, no. 3 (September 1, 2008): 553–69. https://doi.org/10.1137/060667980.
Catllá AJ, Schaeffer DG, Witelski TP, Monson EE, Lin AL. On spiking models for synaptic activity and impulsive differential equations. SIAM Review. 2008 Sep 1;50(3):553–69.
Catllá, A. J., et al. “On spiking models for synaptic activity and impulsive differential equations.” SIAM Review, vol. 50, no. 3, Sept. 2008, pp. 553–69. Scopus, doi:10.1137/060667980.
Catllá AJ, Schaeffer DG, Witelski TP, Monson EE, Lin AL. On spiking models for synaptic activity and impulsive differential equations. SIAM Review. 2008 Sep 1;50(3):553–569.
Published In
SIAM Review
DOI
ISSN
0036-1445
Publication Date
September 1, 2008
Volume
50
Issue
3
Start / End Page
553 / 569
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics