Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 177-188.
Title: Global stability, periodic solutions, and optimal control in a
nonlinear differential delay model
Authors: Anatoli F. Ivanov (Pennsylvania State Univ., Lehman, PA, USA)
Musa A. Mammadov (Univ. of Ballarat, Victoria, Australia)
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.