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Li-Yorke chaos in models with backward dynamics

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  • Stockman David R.

    (University of Delaware – Economics, Newark, DE 19716, USA, Phone: +302-831-1903)

Abstract

Some economic models like the cash-in-advance model of money, the overlapping generations model and a model of credit with limited commitment may have the property that the dynamical system characterizing equilibria in the model are multi-valued going forward in time, but single-valued going backward in time. Such models or dynamical systems are said to have backward dynamics. In such instances, what does it mean for a dynamical system (set-valued) to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, I provide a definition of chaos that is in the spirit of Li and Yorke for a dynamical system with backward dynamics. I utilize the theory of inverse limits to provide sufficient conditions for such a dynamical system to be Li-Yorke chaotic.

Suggested Citation

  • Stockman David R., 2016. "Li-Yorke chaos in models with backward dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(5), pages 587-606, December.
    • Handle: RePEc:bpj:sndecm:v:20:y:2016:i:5:p:587-606:n:6
    DOI: 10.1515/snde-2015-0076
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    References listed on IDEAS

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    1. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
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    Cited by:

    1. Lvlin Luo, 2020. "Noncommutative Functional Calculus and Its Applications on Invariant Subspace and Chaos," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    2. Lvlin Luo, 2021. "The Topological Entropy Conjecture," Mathematics, MDPI, vol. 9(4), pages 1-17, February.

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    More about this item

    Keywords

    backward dynamics; cash-in-advance; inverse limits; limited commitment; Li-Yorke chaos; overlapping generations;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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