The business cycle model with a unique stable limit cycle

Kazuyuki Sasakura*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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
Issue number9-10
Publication statusPublished - 1996


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

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics


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