The business cycle model with a unique stable limit cycle

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    Abstract

    This paper provides the mathematical foundation to the long-standing academic belief that Goodwin's 1951 nonlinear business cycle model has a unique stable limit cycle. In spite of the asymmetric nonlinearity of investment function, the model has certainly a unique stable limit cycle in an economically meaningful region. Once solution paths start from any initial point in the region, they all tend to the limit cycle without escaping from the region or hitting the ceiling or floor of investment during a transition period. The structural stability of the model prevents the limit cycle from vanishing in the face of small perturbations.

    Original languageEnglish
    Pages (from-to)1763-1773
    Number of pages11
    JournalJournal of Economic Dynamics and Control
    Volume20
    Issue number9-10
    Publication statusPublished - 1996 Sep

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    Keywords

    • Asymmetric rayleigh-type equation
    • Goodwin's 1951 model
    • Structural stability
    • Unique stable limit cycle

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Control and Optimization

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