Chaotic equilibria in models with backward dynamics

Judy A. Kennedy and David Stockman

Journal of Economic Dynamics and Control, 2008, vol. 32, issue 3, 939-955

Abstract: Some economic models like the cash-in-advance model of money or overlapping generations model 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, i.e., the model or dynamical system has 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, we provide a definition of chaos that is in the spirit of Devaney for a dynamical system with backward dynamics. We utilize the theory of inverse limits to provide necessary and sufficient conditions for such a dynamical system to be chaotic.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:32:y:2008:i:3:p:939-955

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