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

Computational Economics - Tập 32 - Trang 221-244 - 2008
Cees Diks1, Cars Hommes1, Valentyn Panchenko2, Roy van der Weide3
1CeNDEF, Department of Quantitative Economics, University of Amsterdam, Amsterdam, the Netherlands
2School of Economics, University of New South Wales, Sydney, Australia
3The World Bank, Washington, USA

Tóm tắt

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.

Tài liệu tham khảo

Arrowsmith D.K., Place C.M. (1995) An introduction to dynamical systems. Cambridge University Press, Cambridge Boldrin M., Woodford M. (1990) Equilibrium models displaying endogenous fluctuations and chaos: A survey. Journal of Monetary Economics 25: 189–222 Brock W.A., Hommes C.H. (1997) A rational route to randomness. Econometrica 65: 1059–1095 Brock W.A., Hsieh D.A., LeBaron B. (1991) Nonlinear dynamics, chaos and instability: Statistical theory and economic evidence. MIT Press, Cambridge Chiarella C. (1988) The cobweb model: Its instability and the onset of chaos. Economic Modeling 5: 377–384 Day R.H. (1994) Complex economic dynamics. Volume I: An introduction to dynamical systems and market mechanisms. MIT Press, Cambridge Devaney R.L. (1989) An introduction to chaotic dynamical systems (2nd ed). Addison Wesley Publication, Redwood City 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 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 Grandmont J.-M. (1985) On endogenous competitive business cycles. Econometrica 53: 995–1046 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 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 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 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 Kuznetsov Y. (1995) Elements of applied bifurcation theory. Springer Verlag, New York 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 Medio A. (1992) Chaotic dynamics. Theory and applications to economics. Cambridge University Press, Cambridge Medio A., Lines M. (2001) Nonlinear dynamics: A primer. Cambridge University Press, Cambridge Mira C., Gardini L., Barugola A., Cathala J.-C. (1996) Chaotic dynamics in two-dimensional noninvertible maps. World Scientific, Singapore Muth J.F. (1961) Rational expectations and the theory of price movements. Econometrica 29: 315–335 Nerlove M. (1958) Adaptive expectations and cobweb phenomena. Quarterly Journal of Economics 72: 227–240 Nowak M., May R.M. (1992) Evolutionary games and spatial chaos. Nature 359: 826–929 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 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 Racine J. (2006) gnuplot 4.0: A portable interactive plotting utility. Journal of Applied Econometrics 21: 133–141 Rosser J.B. (2000) From catastrophe to chaos: A general theory of economic discontinuities. Kluwer, Boston Wolf A., Swift J.B., Swinney L., Vastano J.A. (1985) Determining Lyapunov exponents from a time series. Physica D 16: 285–317