Catastrophes and Chaos in Business Cycle Theory

• Authors: A. Jakimowicz
• Languages of publication: EN

Abstracts

EN

The primary thesis of this paper is that a nonlinear dynamical systems theory provides a basis for conducting all kinds of comparisons in the theory of business cycles, and it also enables its further development. A cognitive aim was to show that applying the theory of bifurcations and morphogenesis in the domain of economic fluctuations allows us to construct models of the cycle with greater explicatory and utility values than there were so far. In this way, the precision and consistency of the theory increases. In this field, applications of catastrophe theory are of great importance. Another fact was indicated, namely the theory of deterministic chaos places the issues of explanation and forecasting in economics in a totally different light. It turns out that we are dealing with at least three sources of complexity in economic systems: chaotic attractors, invariant chaotic sets that are not attracting in the form of chaotic saddles and the effects of fractal basin boundaries. This, in turn, limits the effectiveness of traditional economic policy. Economic management should be based on procedures that lower complexity of economic systems, however sometimes lower complexity incurs bigger instability. The paper is a survey of applications of nonlinear dynamical systems to mathematical business cycle models. The survey encompasses both earlier models that were built in 1970s, as well as later concepts. The paper also features a few of my newest results of numerical studies of some nonlinear economic systems.

Keywords

EN

05.45.-a; 89.20.-a; 89.65.Gh; 89.75.-k

Discipline

• 05.45.-a: Nonlinear dynamics and chaos(see also section 45 Classical mechanics of discrete systems; for chaos in fluid dynamics, see 47.52.+j; for chaos in superconductivity, see 74.40.De)
• 89.75.-k: Complex systems(for complex chemical systems, see 82.40.Qt; for biological complexity, see 87.18.-h)
• 89.20.-a: Interdisciplinary applications of physics
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 117
• Issue: 4
• Pages: 640-646

Dates

published

2010-04

Contributors

author

A. Jakimowicz

• The University of Economy, Garbary 2, PL-85-229 Bydgoszcz, Poland

References

• 1. R. Thom, Structural Stability and Morphogenesis. An Outline of a General Theory of Models, Benjamin, London 1975
• 2. R. Gilmore, Catastrophe Theory for Scientists and Engineers, Dover Publications, New York 1993
• 3. T. Poston, I. Stewart, Catastrophe Theory and its Applications, Dover Publications, Mineola 1996
• 4. A.E.R. Woodcock, M. Davis, Catastrophe Theory: A Revolutionary Way of Understanding how Things Change, Pelican, London 1980
• 5. D.J.A. Trotman, E.C. Zeeman, in: Structural Stability, the Theory of Catastrophes, and Applications in the Sciences, Ed. P. Hilton, Springer, Berlin 263 (1976)
• 6. A.M. Saperstein, in: Chaos Theory in the Social Sciences: Foundations and Applications, Eds. L.D. Kiel, E. Elliott, The University of Michigan Press, Ann Arbor 139 (2004)
• 7. E.D. Beinhocker, Origin of Wealth: Evolution, Complexity, and the Radical Remaking of Economics, Harvard Business School Press, Boston 2006
• 8. The Complexity Vision and the Teaching of Economics, Ed. D.C. Colander, Edward Elgar Publications, Cheltenham 2000
• 9. The Economy as an Evolving Complex System II, Eds. W.B. Arthur, S. Durlauf, D.A. Lane, Addison-Wesley, Reading 1997
• 10. A. Jakimowicz, Ekonomista 1, 15 (2009)
• 11. M. Gell-Mann, The Quark and the Jaguar: Adventures in the Simple and the Complex, W.H. Freeman, New York 1994
• 12. W.B. Arthur, Complexity 1, 20 (1995)
• 13. W.B. Arthur, Science 284, 107 (1999)
• 14. J.H. Holland, Hidden Order: How Adaptation Builds Complexity, Addison-Wesley, New York 1995
• 15. J.H. Holland, Emergence: From Chaos to Order, Oxford University Press, Oxford 1998
• 16. J.M. Epstein, Nonlinear Dynamics, Mathematical Biology, and Social Science, Addison-Wesley, Reading 1997
• 17. J.M. Epstein, Generative Social Science: Studies in Agent-Based Computational Modeling, Princeton University Press, Princeton 2006
• 18. W.B. Arthur, Complexity in the Economy and Business, IBM Almaden Institute, San Jose 2007
• 19. P. Mirowski, More Heat than Light: Economics as Social Physics, Physics as Nature's Economics, Cambridge University Press, Cambridge 1989
• 20. Natural Images in Economic Thought: 'Markets Read in Tooth and Claw'. Historical Perspectives of Modern Economics. Ed. P. Mirowski, Cambridge University Press, Cambridge 1994
• 21. C. Mesjasz, S.E.E.D. Journal (Semiotics, Evolution, Energy, and Development) 1, No. 2 (2001)
• 22. G. Ribeill, Metra 14, 499 (1975)
• 23. I. Stewart, New Scientist 68, 447 (1975)
• 24. E.C. Zeeman, in: Proceedings of the International Conference on Manifolds and Related Topics in Topology,ed. A. Hattori, University of Tokyo Press, Tokyo 11 (1975)
• 25. J.G.A. Croll, New Scientist 70, 630 (1976)
• 26. H.J. Sussmann, R.S. Zahler, The Sciences 17, 20 (1977)
• 27. H.J. Sussmann, R.S. Zahler, Behavioral Science 23, 383 (1978)
• 28. H.J. Sussmann, R.S. Zahler, Synthese 37, 117 (1978)
• 29. R.S. Zahler, H.J. Sussmann, Nature 269, 759 (1977)
• 30. J.B. Rosser, Jr., Implications for Teaching Macroeconomics of Complex Dynamics, Department of Economics, James Madison University, Harrisonburg 2004
• 31. H.W. Gottinger, in: On the Stability of Contemporary Economic Systems, Eds. O. Kýn, W. Schrettl, Vandenhoeck und Ruprecht, Göttingen 422 (1979)
• 32. E.C. Zeeman, J. Mathematical Economics 1, 39 (1974)
• 33. E.O. Fischer, W. Jammernegg, Review of Economics and Statistics 68, 9 (1986)
• 34. J.B. Rosser, Jr., The Rise and Fall of Catastrophe Theory Applications in Economics: Was the Baby Thrown Out with the Bathwater?, Thirteenth Annual Symposium of the Society for Nonlinear Dynamics and Econometrics, City University, London 2005
• 35. A. Jakimowicz, Od Keynesa do teorii chaosu. Ewolucja teorii wahań koniunkturalnych, Wydawnictwo Naukowe PWN, Warszawa 2005 (in Polish)
• 36. J.B. Rosser, Jr., From Catastrophe to Chaos: A General Theory of Economic Discontinuities, Kluwer Acad. Publications, Boston 1992
• 37. C.A. Isnard, E.C. Zeeman, in: The Use of Models in the Social Sciences, ed. L. Collins, Tavistock Publications, London 44 (1976)
• 38. E.C. Zeeman, Catastrophe Theory: Selected Papers, 1972-1977, Addison-Wesley, London 1977
• 39. A. Simonovits, Economics of Planning 24, 27 (1991)
• 40. C.H. Hommes, H.E. Nusse, A. Simonovits, J. Economic Dynamics and Control 19, 155 (1995)
• 41. J.R. Hicks, A Contribution to the Theory of the Trade Cycle, Clarendon Press, Oxford 1951
• 42. J.B. Rosser, Jr., M.V. Rosser, Discrete Dynamics in Nature and Society 1, 269 (1998)
• 43. J.B. Rosser, Jr., M.V. Rosser, S.J. Guastello, R.W. Bond, Nonlinear Dynamics, Psychology, and Life Sciences 5, 345 (2001)
• 44. T. Puu, Annals of Operations Research 37, 169 (1992)
• 45. A. Jakimowicz, Nonlinear Dynamics, Psychology, and Life Sciences 13, 393 (2009)
• 46. R.M. Goodwin, Econometrica 19, 1 (1951)
• 47. H.E. Nusse, J.A. Yorke, Dynamics: Numerical Explorations, Springer, New York 1998
• 48. A. Jakimowicz, Nonlinear Dynamics, Psychology, and Life Sciences 14, 69 (2010)
• 49. H.-W. Lorenz, H.E. Nusse, Chaos, Solitons, and Fractals 13, 957 (2002)
• 50. M. Iansiti, Q. Hu, R.M. Westervelt, M. Tinkham, Phys. Rev. Lett. 55, 746 (1985)

Identifiers

DOI

10.12693/APhysPolA.117.640