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Introduction to Stability Analysis of Discrete Dynamical Systems

Author

Listed:
  • Oded Galor

    (Brown University & Hebrew University)

Abstract

This manuscript analyzes the fundamental factors that govern the qualitative behavior of discrete dynamical systems. It introduces methods of analysis for stability analysis of discrete dynamical systems. The analysis focuses initially on the derivation of basic propositions about the factors that determine the local and global stability of discrete dynamical systems in the elementary context of a one dimensional, first-order, autonomous, systems. These propositions are subsequently generalized to account for stability analysis in a multi-dimensional, higher-order, non-autonomous, nonlinear, dynamical systems.

Suggested Citation

  • Oded Galor, 2004. "Introduction to Stability Analysis of Discrete Dynamical Systems," Macroeconomics 0409011, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpma:0409011
    Note: Type of Document - pdf; pages: 70
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mac/papers/0409/0409011.pdf
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    References listed on IDEAS

    as
    1. Oded Galor & Harl E. Ryder, 1988. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Working Papers 1988-07, Brown University, Department of Economics.
    2. Galor, Oded, 1992. "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System," Econometrica, Econometric Society, vol. 60(6), pages 1351-1386, November.
    3. Galor, Oded & Ryder, Harl E., 1989. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Journal of Economic Theory, Elsevier, vol. 49(2), pages 360-375, December.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Frank Hespeler, 2008. "Solution Algorithm to a Class of Monetary Rational Equilibrium Macromodels with Optimal Monetary Policy Design," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 207-223, April.
    2. Brigitta Toth-Bozo & Laszlo Szalai, 2019. "Political Announcements and Exchange Rate Expectations," World Journal of Applied Economics, WERI-World Economic Research Institute, vol. 5(2), pages 53-66, December.

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    More about this item

    Keywords

    Discrete Dynamical Systems; Difference Equations; Global Stability; Local Stability; Non-Linear Dynamics; Stable Manifolds;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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