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.

Cycles in dynamic economic modelling

MANFREDI, PIETRO ANGELO MANFREDO FRANCESCO;FANTI, LUCIANO
2004-01-01

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.
2004
Manfredi, PIETRO ANGELO MANFREDO FRANCESCO; Fanti, Luciano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/80733
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