- Bifurcations of optimal vector fields
- Mathematics of operations research
- Volume | Issue number
- 40 | 1
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations, as problem parameters are varied. The solutions are represented as the integral curves of a multivalued optimal vector field on state space. Generically, there are three types of integral curves: stable points, open intervals that are forward asymptotic to a stable point and backward asymptotic to an unstable point, and half-open intervals that are forward asymptotic to a stable point and backward asymptotic to an indifference point; the latter are initial states to multiple optimal trajectories. We characterize all bifurcations that occur generically in one- and two-parameter families. Most of these are related to global dynamical bifurcations of the state-costate system of the problem.
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