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Assessing the Local Stability Properties of Discrete Three-Dimensional Dynamical Systems: A Geometrical Approach with Triangles and Planes and an Application with Some Cones

Author

Listed:
  • Jean-Pierre Drugeon

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jean-Paul Barinci

    (UEVE - Université d'Évry-Val-d'Essonne)

Abstract

The difficulties associated with the appraisal of the determinacy properties of a three-dimensional system are circumvented by the introduction of a new geometrical argument. It brings about a complete typology of the eigenvalues moduli in discrete time three-dimensional dynamical systems and then provides a new apparatus for assessing from a geometrical standpoint the emergence of local bifurcations for parameterised economies. The argument is considered through the extensive characterisation of the stability properties of a benchmark model of inter-temporal economic analysis.

Suggested Citation

  • Jean-Pierre Drugeon & Jean-Paul Barinci, 2017. "Assessing the Local Stability Properties of Discrete Three-Dimensional Dynamical Systems: A Geometrical Approach with Triangles and Planes and an Application with Some Cones," Post-Print halshs-01884337, HAL.
    • Handle: RePEc:hal:journl:halshs-01884337
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    Citations

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    Cited by:

    1. Stefano Bosi & David Desmarchelier, 2017. "A simple method to study local bifurcations of three and four-dimensional systems: characterizations and economic applications," Working Papers of BETA 2017-07, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    2. Bosi, Stefano & Desmarchelier, David, 2019. "Local bifurcations of three and four-dimensional systems: A tractable characterization with economic applications," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 38-50.
    3. Barinci, Jean-Paul & Cho, Hye-Jin & Drugeon, Jean-Pierre, 2021. "On equilibrium elasticities of substitution in simple overlapping generations economies with heterogeneous goods," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 120-137.

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