Global asymptotic stability in a class of nonlinear differential delay equations

Pages: 727 - 736, Issue Special, September 2011

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Anatoli F. Ivanov - Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA 18627, United States (email)
Musa A. Mammadov - Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, Mt. Helen Campus, PO Box 663, Ballarat, Victoria 3353, Australia (email)

Abstract: 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:  Nonlinear di erential delay equations, Singular perturbations, Global asymptotic stability, Reduction to multi-valued discrete maps, Interval maps
Mathematics Subject Classification:  Primary: 34K20, 34K26; Secondary: 37E05

Received: August 2010;      Revised: January 2011;      Published: October 2011.