Phase Portraits of Stabilized Hamiltonian Systems in Growth Models

Abstract

The paper investigates a qualitative behavior of solutions of Hamiltonian systems generated by the Pontryagin maximum principle for the optimal control problems at the infinite time horizon. Based on the stabilization procedure, authors show that the only possible portraits are stable focus or saddle. As an example, the resource consumption model is considered. By varying the discount factor in the model, authors demonstrate phase portraits in the corresponding optimal control problem. © 2022 American Institute of Physics Inc.. All rights reserved.