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A. Steindl, G. Feichtinger:
"Bifurcations to Periodic Solutions in a Production/Inventory Model";
Journal of Nonlinear Science, 14 (2004), 6; S. 469 - 503.

Total production costs sometimes show an S-shaped form. There are several ways in which a plant with given capacity can be adapted to a specific demand rate, one of them being adaptation of intensity per work hour. In this paper we present an application of the Hamilton-Hopf bifurcation to an inventory/production intensity splitting model with a nonconvex cost function. Our analysis provides a new proof that persistent oscillations may be optimal for arbitrary small discount rates. For zero discounting a "Hamilton Hopf bifurcation" occurs, leading to a family of periodic solutions bifurcating from a steady state. If the discount rate becomes positive, almost all periodic solutions vanish; only a unique branch of periodic solutions is obtained.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04968941

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