Skip to main content

E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics

Abstract

The use of nonlinear dynamic models in economics and finance has expanded rapidly in the last two decades. Numerical simulation is crucial in the investigation of nonlinear systems. E&F Chaos is an easy-to-use and freely available software package for simulation of nonlinear dynamic models to investigate stability of steady states and the presence of periodic orbits and chaos by standard numerical simulation techniques such as time series, phase plots, bifurcation diagrams, Lyapunov exponent plots, basin boundary plots and graphical analysis. The package contains many well-known nonlinear models, including applications in economics and finance, and is easy to use for non-specialists. New models and extensions or variations are easy to implement within the software package without the use of a compiler or other software. The software is demonstrated by investigating the dynamical behavior of some simple examples of the familiar cobweb model, including an extension with heterogeneous agents and asynchronous updating of strategies. Simulations with the E&F Chaos software quickly provide information about local and global dynamics and easily lead to challenging questions for further mathematical analysis.

References

  • Arrowsmith D.K., Place C.M. (1995) An introduction to dynamical systems. Cambridge University Press, Cambridge

    Google Scholar 

  • Boldrin M., Woodford M. (1990) Equilibrium models displaying endogenous fluctuations and chaos: A survey. Journal of Monetary Economics 25: 189–222

    Article  Google Scholar 

  • Brock W.A., Hommes C.H. (1997) A rational route to randomness. Econometrica 65: 1059–1095

    Article  Google Scholar 

  • Brock W.A., Hsieh D.A., LeBaron B. (1991) Nonlinear dynamics, chaos and instability: Statistical theory and economic evidence. MIT Press, Cambridge

    Google Scholar 

  • Chiarella C. (1988) The cobweb model: Its instability and the onset of chaos. Economic Modeling 5: 377–384

    Article  Google Scholar 

  • Day R.H. (1994) Complex economic dynamics. Volume I: An introduction to dynamical systems and market mechanisms. MIT Press, Cambridge

    Google Scholar 

  • Devaney R.L. (1989) An introduction to chaotic dynamical systems (2nd ed). Addison Wesley Publication, Redwood City

    Google Scholar 

  • Diks C.G.H., Weide R. (2005) Herding, a-synchronous updating and heterogeneity in memory in a CBS. Journal of Economic Dynamics and Control 29: 741–763

    Article  Google Scholar 

  • Doedel, E. J., Paffenroth, R. C., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Oldeman, B. E., Sandstede, B., & Wang, X. J. (2001). AUTO2000: Continuation and bifurcation software for ordinary differential equations. Applied and Computational Mathematics. California Institute of Technology. http://indy.cs.concordia.ca/auto/.

  • Ezekiel M. (1938) The cobweb theorem. Quarterly Journal of Economics 52: 255–280

    Article  Google Scholar 

  • Grandmont J.-M. (1985) On endogenous competitive business cycles. Econometrica 53: 995–1046

    Article  Google Scholar 

  • Grandmont, J.-M. (1988). Nonlinear difference equations, bifurcations and chaos: An introduction. CEPREMAP Working Paper No 8811, June 1988.

  • Guckenheimer J., Holmes P. (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer Verlag, New York

    Google Scholar 

  • Hommes, C. H. (1991). Chaotic dynamics in economic models. Some simple case-studies. Groningen Theses in Economics, Management & Organization, Wolters-Noordhoff, Groningen.

  • Hommes C.H. (1994) Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand. Journal of Economic Behavior & Organization 24: 315–335

    Article  Google Scholar 

  • Hommes, C. H. (2006). Heterogeneous agent models in economics and finance, In L. Tesfatsion & K. L. Judd (eds.), Handbook of computational economics, volume 2: Agent-based computational economics (pp. 1109–1186). Amsterdam: North-Holland, Chap. 23.

  • Hommes C.H., Huang H., Wang D. (2005) A robust rational route to randomness in a simple asset pricing model. Journal of Economic Dynamics and Control 29: 1043–1072

    Article  Google Scholar 

  • Huberman B.A., Glance N.S. (1993) Evolutionary games and computer simulations. Proceedings of the National Academy of Sciences of the United States of America 90: 7716–7718

    Article  Google Scholar 

  • Kuznetsov Y. (1995) Elements of applied bifurcation theory. Springer Verlag, New York

    Google Scholar 

  • LeBaron, B. (2006), Agent-based computational finance. In L. Tesfatsion & K. L. Judd (eds.), Handbook of computational economics, volume 2: Agent-based computational economics (pp. 1187–1233). Amsterdam: North-Holland, Chap. 24.

  • Li T.Y., Yorke J.A. (1975) Period three implies chaos. American Mathematical Monthly 82: 985–992

    Article  Google Scholar 

  • Medio A. (1992) Chaotic dynamics. Theory and applications to economics. Cambridge University Press, Cambridge

    Google Scholar 

  • Medio A., Lines M. (2001) Nonlinear dynamics: A primer. Cambridge University Press, Cambridge

    Google Scholar 

  • Mira C., Gardini L., Barugola A., Cathala J.-C. (1996) Chaotic dynamics in two-dimensional noninvertible maps. World Scientific, Singapore

    Google Scholar 

  • Muth J.F. (1961) Rational expectations and the theory of price movements. Econometrica 29: 315–335

    Article  Google Scholar 

  • Nerlove M. (1958) Adaptive expectations and cobweb phenomena. Quarterly Journal of Economics 72: 227–240

    Article  Google Scholar 

  • Nowak M., May R.M. (1992) Evolutionary games and spatial chaos. Nature 359: 826–929

    Article  Google Scholar 

  • Nowak M., Bonhoeffer S., May R.M. (1992) Spatial and the maintainance of cooperation. Proceedings of the National Academy of Sciences of the United States of America 91: 4877–4881

    Article  Google Scholar 

  • Nusse, H. E., & Yorke, J. A. (1998). Dynamics: Numerical explorations (2nd ed.). Applied Mathematical Sciences (Vol. 101). Springer-Verlag.

  • Palis J., Takens F. (1993) Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations. Cambridge University Press, Cambridge

    Google Scholar 

  • Racine J. (2006) gnuplot 4.0: A portable interactive plotting utility. Journal of Applied Econometrics 21: 133–141

    Article  Google Scholar 

  • Rosser J.B. (2000) From catastrophe to chaos: A general theory of economic discontinuities. Kluwer, Boston

    Google Scholar 

  • Wolf A., Swift J.B., Swinney L., Vastano J.A. (1985) Determining Lyapunov exponents from a time series. Physica D 16: 285–317

    Article  Google Scholar 

Download references

Acknowledgments

This paper was presented at the Fourth Workshop Modelli Dinamici in Economia e Finanza, September 21–23, 2006, Urbino, Italy. We thank all participants for helpful comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cees Diks.

Rights and permissions

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Cite this article

Diks, C., Hommes, C., Panchenko, V. et al. E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics. Comput Econ 32, 221–244 (2008). https://doi.org/10.1007/s10614-008-9130-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-008-9130-x

Keywords

  • Nonlinear dynamics
  • Simulation software
  • Heterogeneous agents

JEL Classification

  • C60
  • E37
  • G10