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

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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.

Original languageEnglish (US)
Article numberA177
Pages (from-to)177-188
Number of pages12
JournalElectronic Journal of Differential Equations
Volume19
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • Analysis

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