DNS Curves in a Production/Inventory Model

In this paper, we investigate the bifurcation behavior of an inventory/production model close to a Hamilton-Hopf bifurcation. We show numerically that two different types of DNS curves occur: If the initial states are far from the bifurcating limit cycle, the limit cycle can be approached along diff...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 128; no. 2; pp. 295 - 308
Main Authors Feichtinger, G, Steindl, A
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.02.2006
Subjects
Attraction
Bifurcations
Control theory
Cost engineering
Costs
Eigenvalues
Equilibrium
Inventories
Mathematical models
Optimization
Optimization algorithms
Optimization techniques
Stockpiling
Studies
Trajectories
Variables
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Summary:In this paper, we investigate the bifurcation behavior of an inventory/production model close to a Hamilton-Hopf bifurcation. We show numerically that two different types of DNS curves occur: If the initial states are far from the bifurcating limit cycle, the limit cycle can be approached along different trajectories with the same cost. For a subcritical bifurcation scenario, the hyperbolic equilibrium state and the hyperbolic limit cycle coexist for some parameter range. When both the long term states yield approximately the same cost, a second DNS curve separates their domains of attraction. At the intersection of these two DNS curves, a threefold Skiba point in the state space is found.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-006-9017-8