Bifurcations of Optimal Vector Fields

Tatiana Kiseleva and Florian Wagener

No 11-05, CeNDEF Working Papers from Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance

Abstract: 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 multi-valued `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.

Date: 2011
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Citations: View citations in EconPapers (12)

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