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Journal of Optimization Theory and Applications

, Volume 128, Issue 2, pp 333–353 | Cite as

Business–Cycle Models and the Dangers of Linearizing

  • O. Kozlovski
  • P. Pintus
  • S. van Strien
  • R. de Vilder
Article

Abstract

This paper studies the consequences of linearizing nonlinear business–cycle models near their interior steady state. It is shown that dynamic objects, created for example in a Bogdanov-Takens bifurcation, may be lost in the linearization procedure. Sufficient conditions are provided ensuring the absence of various dynamic features in the nonlinear version of the model.

Keywords

Nonlinear dynamical systems linearization Bogdanov-Takens bifurcation chaos 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • O. Kozlovski
    • 1
  • P. Pintus
    • 2
  • S. van Strien
    • 1
  • R. de Vilder
    • 3
    • 4
  1. 1.Department of MathematicsWarwick UniversityWarwickUK
  2. 2.GREQAM and Department of EconomicsUniversité de la Mediterranée Aix-Marseille IIMarseilleFrance
  3. 3.DELTA-CNRS-EHESS-ENSParisFrance
  4. 4.Department of MathematicsUniversity of AmsterdamAmsterdamNetherlands

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