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

Author

Listed:
  • Piero Manfredi
  • Luciano Fanti

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.

Suggested Citation

  • Piero Manfredi & Luciano Fanti, 2003. "Cycles in continuous-time economic models (with applications to Goodwin's and Solow's models)," Discussion Papers 2003/9, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    • Handle: RePEc:pie:dsedps:2003/9
    Note: ISSN 2039-1854
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    File URL: https://www.ec.unipi.it/documents/Ricerca/papers/2003-9.pdf
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    Cited by:

    1. Pompeo Della Posta, 2003. "Optimal Monetary Instruments and Policy Games Reconsidered," Discussion Papers 2003/12, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.

    More about this item

    Keywords

    Dynamic economic modelling; business and growth cycles; Hopf bifurcations; delay models;
    All these keywords.

    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General

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