Vertical and Horizontal Models in Chaos Theory

  • Lena C. Zuchowski
Part of the New Directions in the Philosophy of Science book series (NDPS)


I will review material on vertical and horizontal modelling. The vertical and horizontal construction of models in chaos theory will be demonstrated in two case studies: the construction of three models based on the logistic equation and two models based on the Lorenz equations.


chaos logistic model Lorenz model models in science 


  1. K. T. Alligood, T. D. Sauer, and J. A. Yorke. Chaos: An Introduction to Dynamical Systems. Springer, New York, 1997.CrossRefGoogle Scholar
  2. D. M. Bailer-Jones. Scientists’ thoughts on scientific models. Perspectives on Science, 10: 275–301, 2002.CrossRefGoogle Scholar
  3. A. Bokulich. Horizontal models: From bakers to cats. Philosophy of Science, 70:609–627, 2003.CrossRefGoogle Scholar
  4. A. Bolinska. Epistemic representation, informativeness and the aim of faithful representation. Synthese, 190: 219–234, 2013.CrossRefGoogle Scholar
  5. N. Cartwright. How the Laws of Physics Lie. Clarendon, Oxford, 1983.CrossRefGoogle Scholar
  6. G. Contessa. Scientific models and fictional objects. Synthese, 172: 215–229, 2010.CrossRefGoogle Scholar
  7. R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison Wesley, Redwood City, 1989.Google Scholar
  8. R. Frigg. Models and fiction. Synthese, 172: 251–268, 2010.CrossRefGoogle Scholar
  9. Roman Frigg and Stephan Hartmann. Models in science. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy, Fall edition, 2012.Google Scholar
  10. R. N. Giere. Explaining Science: A Cognitive Approach. The University of Chicago Press, Chicago, US, 1988.CrossRefGoogle Scholar
  11. P. Godfrey-Smith. Models and fictions in science. Philosophical Studies, 143: 101–116, 2009.CrossRefGoogle Scholar
  12. J. Guckenheimer. A strange, strange attractor. In J. E. Marsden and M. Mc-Cracken, editors, The Hopf Bifurcation and Its applications, pages 368–381. Springer, Berlin, 1976.CrossRefGoogle Scholar
  13. J. Guckenheimer, G. Oster, and A. Ipaktchi. The dynamics of density dependent population models. Journal of Mathematical Biology, 4: 101–147, 1977.CrossRefGoogle Scholar
  14. R. C. Hilborn. Chaos and Nonlinear Dynamics. Oxford University Press, Oxford, 2002.Google Scholar
  15. M. W. Hirsch, S. Smale, and R. L. Devaney. Differential Equations, Dynamical Systems and An Introduction to Chaos. Elsevier, Amsterdam, 2004.Google Scholar
  16. S. H. Kellert. In the Wake of Chaos. The University of Chicago Press, Chicago, 1993.CrossRefGoogle Scholar
  17. S. H. Kellert, M. Stone, and A. Fine. Models, chaos and goodness of fit. Philosophical Topics, 18: 85–106, 1990.CrossRefGoogle Scholar
  18. J. Koperski. Models, confirmation and chaos. Philosophy of Science, 65: 624–649, 1998.CrossRefGoogle Scholar
  19. A. Levy. Modeling without models. Philosophical Studies, 172: 781–798, 2015.CrossRefGoogle Scholar
  20. T.-Y. Li and J. A. Yorke. Period three implies chaos. The American Mathematical Monthly, 82: 985–992, 1975.CrossRefGoogle Scholar
  21. E. Lorenz. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20: 130–141, 1963.CrossRefGoogle Scholar
  22. R. M. May. Biological populations with non-overlapping generations: Stable points, stable Cycles, and chaos. Science, 15: 645–647, 1974.CrossRefGoogle Scholar
  23. R. M. May and G. F. Osler. Bifurcations and dynamic complexity in simple ecological models. The American Naturalist, 110: 573–599, 1976.CrossRefGoogle Scholar
  24. G. Schurz. Kinds of unpredictability in deterministic systems. In P. Weingartner and G. Schurz, editors, Law and Prediction in the Light of Chaos Research, pages 123–141. Springer, Heidelberg, 1996.CrossRefGoogle Scholar
  25. P. Smith. Explaining Chaos. Cambridge University Press, Cambridge, 1998.CrossRefGoogle Scholar
  26. M. Suarez. Fictionals, conditionals and stellar astrophysics. International Studies in the Philosophie of Science, 27: 235–252, 2013.CrossRefGoogle Scholar
  27. A. Toon. Models as Make Believe: Imagination, Fiction and Scientific Representation. New Directions in Philosophy of Science. Palgrave Macmillan, Basingstoke, UK, 2012.CrossRefGoogle Scholar
  28. M. Viana. What’s new on Lorenz strange attractors. The Mathematical Intelligencer, 22: 6–18, 2000.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Lena C. Zuchowski
    • 1
  1. 1.Fachbereich PhilosophieUniversität SalzburgSalzburgAustria

Personalised recommendations