 A Geometric Approach to Local Indeterminacy & Local Bifurcations in Three-Dimensional Dynamical SystemsJ.-P. Barinci and J.-P. Drugeon Papiers d'Economie Mathématique et Applications from Université Panthéon-Sorbonne (Paris 1) Abstract: In discrete three-dimensional dynamical systems frequently encountered in dynamic general equilibrium models, local indeterminacy -sunspot equilibria - and local bifurcations -endogenous deterministic fluctuations - issues are quite difficult to handle. Pitfalls derive from the fact that in generic models a standard analysis of the spectrum of the 3 x 3 Jacobian matrix, though achievable, usually turns out to be of no use. It is the purpose of this contribution to develop geometrical tools which avoid cumbersome computations or numerical investigations. Rather tractable necessary and sufficient conditions are provided, that ensure the occurence of generic local bifurcations and also a useful "toolkit" for assessing the local determinacy / indeterminacy of intertemporal equilibria. The usefulness of this method is finally illustrated in a productive model of overlapping generations with elastic labour supply. Keywords: BUSINESS CYCLES; MATHEMATICAL ANALYSIS; ECONOMIC GROWTH (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:fth:pariem:1999.40 Access Statistics for this paper More papers in Papiers d'Economie Mathématique et Applications from Université Panthéon-Sorbonne (Paris 1) France; Universite de Paris I - Pantheon- Sorbonne, 12 Place de Pantheon-75005 Paris, France. Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.