Stability conditions for singularly perturbed delay differential equations

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2 Citations (Scopus)

Abstract

Singular perturbation problems containing a small positive parameter ε occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. A uniformly valid, reliable interpretable approximation of such problems is required. This paper provides sufficient conditions to ensure the exponential stability of the analytical and numerical solutions of the singularly perturbed delay differential equations with a bounded time-lag for suf.ciently small ε > 0. The Halanay inequality is used to prove the main results of the paper. A numerical example is provided to illustrate the methodology and clarify the need for a stiff solver for numerical solutions of these problems.

Original languageEnglish
Pages (from-to)292-303
Number of pages12
JournalComputational Mathematics and Modeling
Volume19
Issue number3
DOIs
Publication statusPublished - Jul 1 2008
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics

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