Safia Acher Spitalier, Rachid Bebbouchi
Abstract:
We study a family of singularly perturbed ODEs with one parameter
and compare their solutions to the ones of the corresponding reduced
equations. The interesting characteristic here is that the reduced
equations have more than one solution for a given set of initial conditions.
Then we consider how those solutions are organized for different values of the
parameter. The bifurcation associated to this situation is studied
using a minimal set of tools from non standard analysis.
Submitted July 10, 2016. Published October 17, 2016.
Math Subject Classifications: 34A26, 34C05, 34D15, 34F10.
Key Words: Singular perturbation; reduced equation with non-uniqueness;
bifurcation; non-standard analysis.
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Safia Acher Spitalier Université des Sciences et de la Technologie Houari Boumediene Faculté des Mathématiques BP 32 EL ALIA 16111 Bab Ezzouar Alger, Algérie email: safia.acher.spitalier@gmail.com |
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Rachid Bebbouchi Université des Sciences et de la Technologie Houari Boumediene Faculté des Mathématiques BP 32 EL ALIA 16111 Bab Ezzouar Alger, Algérie email: rbebbouchi@hotmail.com |
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