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NONLINEAR AND COMPLEX DYNAMICS IN ECONOMICS

Published online by Cambridge University Press:  07 November 2014

William A. Barnett
Affiliation:
University of Kansas
Apostolos Serletis*
Affiliation:
University of Calgary
Demitre Serletis
Affiliation:
University of Arkansas for Medical Sciences
*
Address correspondence to: Apostolos Serletis, Department of Economics, University of Calgary, Calgary, Alberta T2N 1N4, Canada; e-mail: Serletis@ucalgary.ca; URL: http://econ.ucalgary.ca/serletis.htm.

Abstract

This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

Type
Articles
Copyright
Copyright © Cambridge University Press 2014 

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