Cycles in continuous-time economic models (with applications to Goodwin's and Solow's models)

Piero Manfredi and Luciano Fanti

Discussion Papers from Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy

Abstract: This paper offers a unified perspective of the analytical detection of Hopf bifurcation, which is a crucial tool in dynamic economic modelling. We clarify the relations between stability theorems and the notions of Simple and General Hopf Bifurcations. A Lienard-Chipart-type theorem for detecting bifurcations, which appears of considerable usefulness in applications, is proved. Subsequently we show how to use the notions of "stability boundary" and "bifurcation boundary", providing a new, surprisingly straightforward, tool for detecting bifurcations in economics. An economic illustration is given by two models with time delay: a Solow-type demo-economic model and a Kaleckian extension of the Lotka-Volterra-Goodwin model.

Keywords: Dynamic economic modelling; business and growth cycles; Hopf bifurcations; delay models (search for similar items in EconPapers)
JEL-codes: E0 (search for similar items in EconPapers)
Date: 2003-01-01
Note: ISSN 2039-1854
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.ec.unipi.it/documents/Ricerca/papers/2003-9.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pie:dsedps:2003/9

Access Statistics for this paper

More papers in Discussion Papers from Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy Contact information at EDIRC.
Bibliographic data for series maintained by ().