Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 177-188.

Global stability, periodic solutions, and optimal control in a nonlinear differential delay model

Anatoli F. Ivanov, Musa A. Mammadov

A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.

Published September 25, 2010.
Math Subject Classifications: 34K13, 34K20, 34K35, 91B55, 92C23.
Key Words: Scalar nonlinear differential delay equations; periodic solutions; global asymptotic stability; Mackey blood cell production model; optimization of consumption; Ramsey economic model with delay.

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Anatoli F. Ivanov
Department of Mathematics
Pennsylvania State University
P.O. Box PSU, Lehman, PA 18627, USA
email: afi1@psu.edu
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: m.mammadov@ballarat.edu.au

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