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Hopf bifurcation and quasi-periodic dynamics in discrete multisector optimal growth models

Authors
Journal
Ricerche Economiche
0035-5054
Publisher
Elsevier
Publication Date
Volume
50
Issue
3
Identifiers
DOI: 10.1006/reco.1996.0018
Keywords
  • Optimal Growth
  • Hopf Bifurcation
  • Quasi-Periodic Optimal Paths
Disciplines
  • Mathematics

Abstract

Abstract This paper discusses the asymptotic stability of the steady state and the existence of a Hopf bifurcation in discrete time multisector optimal growth models. We obtain on the one hand a local turnpike theorem which guarantees the saddle point property for all discount rates. On the other hand, we provide a new proposition which gives some conditions ensuring local stability of the steady state if the impatience rate is not too high. A characterization of the bound δ*, above which the steady state is saddle-point stable, is also proposed in terms of indirect utility function's concavity properties. On this basis, some sufficient conditions for the existence of a Hopf bifurcation are stated. We thus prove the existence of quasi-periodic optimal paths in asymmetric models.

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