DNS (Dechert, Nishimura, and Skiba) 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 Dechert, Nishimura, and Skiba (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.