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DNS curves in a production/inventory model. (English) Zbl 1181.49038
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.

MSC:
49N90 Applications of optimal control and differential games
90B05 Inventory, storage, reservoirs
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37N40 Dynamical systems in optimization and economics
90B30 Production models
91B62 Economic growth models
Software:
BNDSCO
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References:
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