Global asymptotic stability in a class of nonlinear differential delay equations

Anatoli F. Ivanov; Musa A. Mammadov

doi:10.3934/proc.2011.2011.727

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2011, Volume 2011: 727-736. Doi: 10.3934/proc.2011.2011.727 open access

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Global asymptotic stability in a class of nonlinear differential delay equations

Anatoli F. Ivanov^1, and
Musa A. Mammadov^2,

1.
Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA 18627
2.
Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, Mt. Helen Campus, PO Box 663, Ballarat, Victoria 3353

Received: August 2010

Revised: January 2011

Published: August 2017

Abstract / Introduction Related Papers Cited by

Abstract

An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are derived. An application to a physiological model by M.C. Mackey is treated in detail.

Keywords:

Nonlinear dierential delay equations,
Singular perturbations,
Global asymptotic stability,
Reduction to multi-valued discrete maps,
Interval maps.

Mathematics Subject Classification: Primary: 34K20, 34K26; Secondary: 37E05.

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