Li-Yorke chaos in models with backward dynamics

David Stockman

Studies in Nonlinear Dynamics & Econometrics, 2016, vol. 20, issue 5, 587-606

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.

Keywords: backward dynamics; cash-in-advance; inverse limits; limited commitment; Li-Yorke chaos; overlapping generations (search for similar items in EconPapers)
JEL-codes: C6 E3 E4 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1515/snde-2015-0076

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