Global stabilization in nonlinear discrete systems with time-delay
- Authors: Ivanov, Anatoli , Mammadov, Musa , Trofimchuk, Sergei
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol.56, no. 2 (2012), p. 1-13
- Full Text: false
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- Description: A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved. © 2012 Springer Science+Business Media, LLC.
Global asymptotic stability in a class of nonlinear differential delay equations
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.
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- Reviewed:
- Description: An essentially nonlinear dierential 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 de- rived. An application to a physiological model by M.C. Mackey is treated in detail.
- Description: 2003009358
Global stability, periodic solutions and optimal control in a nonlinear differential delay model
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2010
- Type: Text , Conference proceedings
- Relation: Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, 2010
- Full Text: false
- Description: A nonlinear differential equation with delay serving as a mathematical model of several applied problmes 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 Ramsay. An optimization problem for a maximal consumption is stated and solved for the latter.