Advertisement

The Logistic Map: An AI Tool for Economists Investigating Complexity and Suggesting Policy Decisions

  • Carmen PagliariEmail author
  • Nicola Mattoscio
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 805)

Abstract

The present contribution contains an original interpretation of the logistic map popularized by the biologist Robert May in 1976. This map is potentially a powerful AI tool based on a deterministic methodology having a double possibility to be applied in economics. The first application is to investigate the intrinsic complexity of real economic phenomena characterized by endogenous non-linear dynamics. The second application is to determine results, typical of a normative science, useful for suggesting policy decisions aimed to avoid chaos and unpredictability in the real economic system. In the first type of application, the logistic map can be used as an AI tool of forecasting (for previsions of bifurcations, cycles and chaos). In the second, the logistic map can be considered as an AI tool for policy makers in order to deduce the analytical conditions that ensure the economic system to be sufficiently far away from chaos and uncontrollability.

Keywords

Economic non-linear dynamics Complexity Chaos Policy decisions Logistic map 

References

  1. 1.
    Alligood, K.T., Sauer, T., Yorke, J.A.: Chaos. An Introduction to Dynamical Systems. Springer, New York (1996)zbMATHGoogle Scholar
  2. 2.
    Andrecut, M.: Logistic map as a random number generator. Int. J. Mod. Phys. B 12(9), 921–930 (1998)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Barkley Rosser, J.: From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Springer, New York (2000)zbMATHGoogle Scholar
  4. 4.
    Baumol, W.J., Benhabib, J.: Chaos: significance, mechanism, and economic applications. J. Econ. Perspect. 3(1), 77–105 (1981)Google Scholar
  5. 5.
    Benhabib, J.: On cycles and chaos in economics. Stud. Nonlinear Dyn. Econom. 1(1), 1–4 (1996)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Benhabib, J., Day, R.H.: Rational choice and erratic behaviour. Rev. Econ. Stud. 48(3), 459–471 (1981)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bullard, J., Butler, A.: Nonlinearity and chaos in economic models: implications for policy decisions. Econ. J. 103(419), 849–867 (1993)Google Scholar
  8. 8.
    Day, R.H.: Irregular growth cycles. Am. Econ. Rev. 72(3), 406–414 (1982)Google Scholar
  9. 9.
    Day, R.H.: The emergence of chaos from classical economic growth. Q. J. Econ. 98(2), 201–213 (1983)MathSciNetGoogle Scholar
  10. 10.
    Day, R.H.: Complex economic dynamics: obvious in history, generic in theory, elusive in data. J. Appl. Econom. 7(Suppl.), 9–23 (1992). Special Issue on Nonlinear Dynamics and EconometricsGoogle Scholar
  11. 11.
    Emmert-Streib, F., Behmer, M.: Optimization procedure for predicting non-linear time series based on a non-Gaussian noise model. In: Gelbukh, A., Fernando, A. (eds.) MICAI 2007: Advances in Artificial Intelligence. Springer, Heidelberg (2007)Google Scholar
  12. 12.
    Faggini, M., Parziale, A.: The failure of economic theory. Lessons from chaos theory. Mod. Econ. 3, 1–10 (2012)Google Scholar
  13. 13.
    Farmer, R.: Deficits and cycles. J. Econ. Theory 40(1), 77–88 (1986)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Fidanova, S., Roeva, O., Mucherino, A., Kapanova, C.: InterCriteria analysis of ant algorithm with environment change for GPS surveying problem. In: Dichev, C., Agre, G. (eds.) Artificial Intelligence: Methodology, Systems, and Applications: AIMSA 2016 Proceedings. Springer, Cham (2016)Google Scholar
  15. 15.
    Grandmont, J.M.: On endogenous competitive business cycles. Econometrica 53(5), 995–1045 (1985)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Grandmont, J.M.: Stabilizing competitive business cycle. J. Econ. Theory 40(1), 57–76 (1986)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Grandmont, J.M.: Nonlinear difference equations, bifurcations and chaos: an introduction. Res. Econ. 62, 122–177 (2008)Google Scholar
  18. 18.
    Holyst, J.A.: How to control a chaotic economy. J. Evol. Econ. 6(1), 31–42 (1996)Google Scholar
  19. 19.
    Holyst, J.A., Urbanowicz, K.: Chaos control in economical model by time delayed feedback method. Physica A 287(3–4), 587–598 (2000)Google Scholar
  20. 20.
    Kaas, L.: Stabilizing Chaos in a Dynamic Macroeconomic Model. J. Econ. Behav. Organ. 33(3–4), 313–332 (1998)Google Scholar
  21. 21.
    Koda, M.: Chaos search in fourier amplitude sensitivity test. J. Inf. Commun. Technol. 11, 1–16 (2012)Google Scholar
  22. 22.
    Kopel, M.: Improving the performance of an economic system: controlling chaos. J. Evol. Econ. 7(3), 269–289 (1997)MathSciNetGoogle Scholar
  23. 23.
    May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)zbMATHGoogle Scholar
  24. 24.
    Medio, A.: Teoria Non-Lineare del Ciclo Economico. Il Mulino, Bologna (1979)Google Scholar
  25. 25.
    Nishimura, K., Sorger, G.: Optimal Cycles and Chaos: A Survey. Stud. Nonlinear Dyn. Econom. 1(1), 11–28 (1996)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Persohn, K.J., Povinelli, R.J.: Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation. Chaos Solitons Fractals 45(3), 238–245 (2012)Google Scholar
  27. 27.
    Thom, R.: Stabilité Structurelle et Morphogénèse. W.A. Benjamin Inc., Massachusetts (1972). English Edition: Structural Stability and Morphogenesis. Westwiew Press, Reading, Massachusetts (1975)Google Scholar
  28. 28.
    Tzouveli, P.K., Ntalianis, K.S., Kollias, S.D.: Chaotic encryption driven watermarking of human video objects based on Hu moments. In: Maglogiannis, I., Karpuozis, K., Bramer, M. (eds.) Artificial Intelligence Applications and Innovations. AIAI 2006 Proceedings. Springer, Boston (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Philosophical, Pedagogical and Economic-Quantitative SciencesUniversity of Chieti-PescaraPescaraItaly

Personalised recommendations