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Published online by Cambridge University Press:  07 November 2014

William A. Barnett
University of Kansas
Apostolos Serletis*
University of Calgary
Demitre Serletis
University of Arkansas for Medical Sciences
Address correspondence to: Apostolos Serletis, Department of Economics, University of Calgary, Calgary, Alberta T2N 1N4, Canada; e-mail:; URL:


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.

Copyright © Cambridge University Press 2014 

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Azariadis, Costas (1993) Intertemporal Macroeconomics. Oxford, UK: Blackwell Publishers.Google Scholar
Barnett, William A., Banerjee, Sanjibani, Duzhak, Evgeniya, and Gopalan, Ramu (2011) Bifurcation analysis of Zellner's marshallian macro model. Journal of Economic Dynamics and Control 35, 15771585.Google Scholar
Barnett, William A. and Duzhak, Evgeniya A. (2007) Hopf bifurcation within new Keynesian functional structure. In Barnett, William A. and Serletis, Apostolos (eds.), Functional Structure Inference, pp. 257275. Oxford, UK: Elsevier.CrossRefGoogle Scholar
Barnett, William A. and Duzhak, Evgeniya A. (2010) Empirical assessment of bifurcation regions within new Keynesian models. Economic Theory 45, 99128.CrossRefGoogle Scholar
Barnett, William A. and Eryilmaz, Unal (2013) Hopf bifurcation in the Clarida, Gali, and Gertler model. Economic Modelling 31, 401404.CrossRefGoogle Scholar
Barnett, William A. and Eryilmaz, Unal (in press) An analytical and numerical search for bifurcations in open economy new Keynesian models. Macroeconomic Dynamics.Google Scholar
Barnett, William A. and Ghosh, Taniya (2013) Bifurcation analysis of an endogenous growth model. Journal of Economic Asymmetries 10, 5364.CrossRefGoogle Scholar
Barnett, William A. and Ghosh, Taniya (in press) Stability analysis of Uzawa–Lucas endogenous growth model. Economic Theory Bulletin.Google Scholar
Barnett, William A. and He, Susan (2010) Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right. Economic Modelling 27, 13451354.CrossRefGoogle Scholar
Barnett, William A. and Hinich, Melvin J. (1992) Empirical chaotic dynamics in economics. Annals of Operations Research 37, 115.CrossRefGoogle Scholar
Barnett, William A., Medio, Alfredo, and Serletis, Apostolos (1997) Nonlinear and Complex Dynamics in Economics. EconWPA working paper.Google Scholar
Barnett, William A. and Serletis, Apostolos (2000) Martingales, nonlinearity, and chaos. Journal of Economic Dynamics and Control 24, 703724.CrossRefGoogle Scholar
Baumol, William and Benhabib, Jess (1989) Chaos: Significance, mechanism, and economic applications. Journal of Economic Perspectives 3, 77106.CrossRefGoogle Scholar
Benhabib, Jess and Day, Richard H. (1981) Rational choice and erratic behavior. Review of Economic Studies 48, 459471.CrossRefGoogle Scholar
Bollerslev, Tim (1986) Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307327.CrossRefGoogle Scholar
Brock, William A. (1988) Nonlinearity and complex dynamics in economics and finance. In Anderson, Philip W., Arrow, Kenneth J., and Pines, David (eds.), The Economy as an Evolving Complex System, pp. 7797. Santa Fe, NM: Addison Wesley.Google Scholar
Brock, William A., Dechert, W. Davis, LeBaron, Blake, and Scheinkmam, José A. (1996) A test for independence based on the correlation dimension. Econometric Reviews 15, 197235.CrossRefGoogle Scholar
Bullard, James and Butler, Alison (1993) Nonlinearity and chaos in economic models: Implications for policy decisions. Economic Journal 103, 849867.CrossRefGoogle Scholar
Day, Richard H. (1982) Irregular growth cycles. American Economic Review 72, 406414.Google Scholar
Engle, Robert F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 9871008.CrossRefGoogle Scholar
Engle, Robert F., Lilien, David M., and Robins, Russell P. (1987) Estimating time varying risk premia in the term structure. Econometrica 55, 391407.CrossRefGoogle Scholar
Fama, Eugene F. (1965) The behavior of stock market prices. Journal of Business 38, 34105.CrossRefGoogle Scholar
Fama, Eugene F. (1970) Efficient capital markets: A review of theory and empirical work. Journal of Finance 25, 383417.CrossRefGoogle Scholar
Feigenbaum, Mitchell J. (1978) Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics 19, 2552.CrossRefGoogle Scholar
Goodwin, Richard M. (1951) The non-linear accelerator and the persistence of business cycles. Econometrica 19, 117.CrossRefGoogle Scholar
Grandmont, Jean-Michel (1985) On endogenous competitive business cycles. Econometrica 53, 9951045.CrossRefGoogle Scholar
Grassberger, Peter and Procaccia, Itamar (1983) Characterization of strange attractors. Physical Review Letters 50, 346349.CrossRefGoogle Scholar
Guckenheimer, John and Holmes, Philip (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer Verlag.CrossRefGoogle Scholar
LeRoy, Stephen F. (1989) Efficient capital markets and martingales. Journal of Economic Literature 27, 15831621.Google Scholar
Li, Tien-Yien and Yorke, James A. (1975) Period three implies chaos. American Mathematical Monthly 82, 985992.CrossRefGoogle Scholar
Lucas, Robert E. Jr., (2009) In defence of the dismal science. The Economist, August 6.Google Scholar
Mandelbrot, Benoit B. (1963) The variation of certain speculative stock prices. Journal of Business 36, 394419.CrossRefGoogle Scholar
Mandelbrot, Benoit B. (1985) Self-affine fractals and fractal dimension. Physica Scripta 32, 257260.CrossRefGoogle Scholar
Matsuyama, Kiminori (1991) Endogenous price fluctuations in an optimizing model of a monetary economy. Econometrica 59, 16171631.CrossRefGoogle Scholar
Medio, Alfredo (1992) Chaotic Dynamics: Theory and Applications to Economics. Cambridge, UK: Cambridge University Press.Google Scholar
Nelson, Daniel B. (1991) Conditional heteroscedasticity in asset returns. Econometrica 59, 347370.CrossRefGoogle Scholar
Samuelson, Paul A. (1965) Proof that properly anticipated prices fluctuate randomly. Industrial Management Review 6, 4149.Google Scholar
Sidrauski, Miguel (1967) Rational choice and patterns of growth in a monetary economy. American Economic Review 57, 534544.Google Scholar
Solow, Robert M. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics 70, 6594.CrossRefGoogle Scholar
Woodford, Michael (1989) Imperfect financial intermediation and complex dynamics. In Barnett, William A., Geweke, John, and Shell, Karl (eds.), Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, pp. 309338. Cambridge, UK: Cambridge University Press.Google Scholar