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G. Feichtinger, A. Steindl:
"DNS Curves in a Production/Inventory Model";
Journal of Optimization Theory and Applications, 128 (2006), 2; 295 - 308.

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.

Optimal control - bifurcation theory - Hamilton-Hopf bifurcation - intensity splitting

http://springerlink.metapress.com/content/h8p1v22g26112173/fulltext.pdf