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On the Characterization of Steady-States in Three-Dimensional Discrete Dynamical Systems

Author

Listed:
  • Amer Tabakovic

    (CREA, Université de Luxembourg)

Abstract

This paper develops a new method to completely characterize the local stability properties of three-dimensional, first-order, nonlinear, autonomous discrete dynamical systems. This is acomplished analytically by means of the characteristic polynomial, i. e., by means of the trace, the determinant, and the sum of principal minors of order two of the Jacobi matrix. The intuition for this method relies on algebraic properties of the (cubic) characteristic polynomial.

Suggested Citation

  • Amer Tabakovic, 2015. "On the Characterization of Steady-States in Three-Dimensional Discrete Dynamical Systems," DEM Discussion Paper Series 15-16, Department of Economics at the University of Luxembourg.
    • Handle: RePEc:luc:wpaper:15-16
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    References listed on IDEAS

    as
    1. Alonso-Carrera, Jaime & Caballe, Jordi & Raurich, Xavier, 2005. "Growth, habit formation, and catching-up with the Joneses," European Economic Review, Elsevier, vol. 49(6), pages 1665-1691, August.
    2. Oded Galor, 2007. "Discrete Dynamical Systems," Springer Books, Springer, edition 1, number 978-3-540-36776-5, September.
    3. Irmen, Andreas & Tabaković, Amer, 2017. "Endogenous capital- and labor-augmenting technical change in the neoclassical growth model," Journal of Economic Theory, Elsevier, vol. 170(C), pages 346-384.
    4. Okuguchi, Koji & Irie, Kazuya, 1990. "The Schur and Samuelson Conditions for a Cubic Equation," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 414-418, December.
    5. Jean-Paul Barinci & Jean-Pierre Drugeon, 2005. "On Outward-Looking Comparison Utility, Heterogeneous Preferences & the Third Dimension: A Geometric Perspective," Documents de recherche 05-07, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
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    More about this item

    Keywords

    Non-Linear Discrete Dynamics; Local Stability Properties;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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