On Tykhonov's Theorem for Convergence of Solutions of Slow and Fast Systems

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dc.contributor.authorLobry, Claude
dc.contributor.authorSari, Tewfik
dc.contributor.authorTouhami, Sefiane
dc.date.accessioned2019-03-25T19:46:15Z
dc.date.available2019-03-25T19:46:15Z
dc.date.issued1998-07-09
dc.description.abstractSlow and fast systems gain their special structure from the presence of two time scales. Their analysis is achieved with the help of Singular Perturbation Theory. The fundamental tool is Tykhonov's theorem which describes the limiting behaviour, for compact interval of time, of solutions of the perturbed system which is a one-parameter deformations of the so-called unperturbed system. Our aim here is to extend this description to the solutions of all systems that belong to a small neighbourhood of the unperturbed system. We investigate also the behaviour of solutions on the infinite time interval. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic approach to Nonstandard Analysis.
dc.description.departmentMathematics
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationLobry, C., Sari, T. & Touhami, S. (1998). On Tykhonov's theorem for convergence of solutions of slow and fast systems. <i>Electronic Journal of Differential Equations, 1998</i>(19), pp. 1-22.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/7939
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 1998, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSingular perturbations
dc.subjectDeformations
dc.subjectAsymptotic stability
dc.subjectNonstandard analysis
dc.titleOn Tykhonov's Theorem for Convergence of Solutions of Slow and Fast Systems
dc.typeArticle

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