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On the Use of the Renormalization Procedure to Estimate the Bifurcation Parameters in Nonlinear Dynamic Models

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  • Walter Briec
  • Laurence Lasselle

Abstract

The renormalization procedure facilitates the detection of periodic and chaotic patterns of many two-dimensional systems of nonlinear equations. We first give a comprehensive presentation of this procedure. We then generalize it to make it more applicable to economic frameworks. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Walter Briec & Laurence Lasselle, 2013. "On the Use of the Renormalization Procedure to Estimate the Bifurcation Parameters in Nonlinear Dynamic Models," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 557-574, April.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:4:p:557-574
    DOI: 10.1007/s10614-012-9356-5
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    References listed on IDEAS

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    1. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    2. Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
    3. Yokoo, Masanori, 2000. "Chaotic dynamics in a two-dimensional overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 909-934, June.
    4. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    5. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    6. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
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    More about this item

    Keywords

    Period-doubling bifurcation; Two-dimensional map; C60; E32;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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