| Popis: |
Goodwin’s celebrated growth cycle model has been widely studied since its introduction in 1967. In recent years several contributions have appeared with the aim of amending the original model so as to improve its economic coherence and enrich its structure. In this article we propose a new and generalized approach, within the theory of planar Hamiltonian systems, for the modeling of Goodwin-type cycles. This new approach, which includes and improves various attempts by the recent literature, is very general and fulfills the essential requirement that the orbits lie entirely in the economically feasible interval. We provide a necessary and sufficient condition for all solutions to be cycles lying entirely in the unit box. In addition, we study the period length of the cycles near the equilibrium and close to the boundary of the domain. Finally, we discuss an example of how small perturbations of the model may affect the qualitative behavior of the solutions. |
