Anatoli F. Ivanov, Musa A. Mammadov
Abstract:
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 |
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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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