American Institute of Mathematical Sciences

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2011, 2011(Special): 727-736. doi: 10.3934/proc.2011.2011.727

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, United States
2. 

Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, Mt. Helen Campus, PO Box 663, Ballarat, Victoria 3353, Australia

Received  August 2010 Revised  January 2011 Published  October 2011

An essentially nonlinear di erential 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: Global asymptotic stability, Reduction to multi-valued discrete maps, Nonlinear di erential delay equations, Interval maps, Singular perturbations.
Mathematics Subject Classification: Primary: 34K20, 34K26; Secondary: 37E05.
Citation: Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727-736. doi: 10.3934/proc.2011.2011.727
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