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Evaluation of Chaotic Models

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A Philosophical Analysis of Chaos Theory

Part of the book series: New Directions in the Philosophy of Science ((NDPS))

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Abstract

I will introduce an analytic framework that conceptualizes the evaluation of vertical chaotic models as consisting of three steps: the determination of the chaotic conditional to be transferred from a model to a target system; the determination of the existence of chaos in the target system; and the evaluation of model faithfulness. Each step will be discussed in detail. I will also discuss the evaluation and investigative role of horizontal chaotic models.

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Bibliography

  • D. Aubin and A. Dahan Dalmedico. Writing the history of dynamical systems and chaos: Longue duree and revolution, disciplines and cultures. Historia Mathematica, 29: 273–339, 2002.

    Article  Google Scholar 

  • R. W. Batterman. Defining chaos. Philosophy of Science, 60: 43–66, 1993.

    Article  Google Scholar 

  • A. Bokulich. Horizontal models: From bakers to cats. Philosophy of Science, 70:609–627, 2003.

    Article  Google Scholar 

  • N. Chernov and R. Markarian. Chaotic Billiards. American Mathematical Society, New York, 2006.

    Book  Google Scholar 

  • J. M. Cushing. Integrodifferential Equations and Delay Models in Population Dynamics. Springer, Berlin, 1977.

    Book  Google Scholar 

  • P. Cvitanovic. Universality in Chaos. Adam Hilger, Bristol, 1986.

    Google Scholar 

  • R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison Wesley, Redwood City, 1989.

    Google Scholar 

  • J. Guckenheimer, G. Oster, and A. Ipaktchi. The dynamics of density dependent population models. Journal of Mathematical Biology, 4: 101–147, 1977.

    Article  Google Scholar 

  • M. P. Hassell, J. H. Lawton, and R. M. May. Patterns of dynamical behavior in single-species populations. Journal of Animal Ecology, 45: 471–486, 1976.

    Article  Google Scholar 

  • A. Hastings, C. L. Hom, S. Ellner, P. Turchin, and H. C. J. Godfrey. Chaos in ecology: Is mother nature a strange attractor? Annual Review of Ecology and Systematics, 24: 1–33, 1993.

    Article  Google Scholar 

  • M. W. Hirsch, S. Smale, and R. L. Devaney. Differential Equations, Dynamical Systems and An Introduction to Chaos. Elsevier, Amsterdam, 2004.

    Google Scholar 

  • S. H. Kellert. A Philosophical evaluation of the chaos theory „revolution. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 33–49, 1992.

    Google Scholar 

  • S. H. Kellert. In the Wake of Chaos. The University of Chicago Press, Chicago, 1993.

    Book  Google Scholar 

  • J. Koperski. Models, confirmation and chaos. Philosophy of Science, 65: 624–649, 1998.

    Article  Google Scholar 

  • M. Kot and W. M. Schaffer. Discrete-time growth-dispersal models. Mathematical Biosciences, 80: 109–136, 1986.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • E. Lorenz. The Essence of Chaos. UCL Press, London, 1993.

    Book  Google Scholar 

  • R. M. May. Biological populations with non-overlapping generations: Stable points, stable Cycles, and chaos. Science, 15: 645–647, 1974.

    Article  Google Scholar 

  • R. M. May. Simple mathematical models with very complicated dynamics. Nature, 261: 459–467, 1976.

    Article  Google Scholar 

  • R. M. May. Spatial chaos and its role in ecology and evolution. In S. A. Levin, editor, Frontiers in Mathematical Biology, pages 326–344. Springer, Berlin, 1994.

    Chapter  Google Scholar 

  • R. M. May and G. F. Osler. Bifurcations and dynamic complexity in simple ecological models. The American Naturalist, 110: 573–599, 1976.

    Article  Google Scholar 

  • Mark McEvoy. Experimental mathematics, computers and the a priori. Synthese, 190: 397–412, 2013.

    Article  Google Scholar 

  • E. Ott, T. Sauer, and J. A. Yorke. Coping with Chaos: Analysis of Chaotic Data and The Exploitation of Chaotic Systems. Wiley, New York, 1994.

    Google Scholar 

  • K. Palmer. Shadowing in Dynamical Systems: Theory and Application. Springer, Boston, 2000.

    Book  Google Scholar 

  • R. Pool. Is it chaos, or is it just noise? Science, 243: 25–28, 1989.

    Article  Google Scholar 

  • R. Robertson and A. Combs. Chaos Theory in Psychology and the Life Sciences. Lawrence Erlbaum, Hove, 1995.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • S. Smale. Differentially dynamical systems. i. diffeomorphisms. Bulletin of the American Mathematical Society, 73: 747–816, 1967.

    Article  Google Scholar 

  • S. Smale. Mathematical problems for the new century. The Mathematical Intelligencer, 20: 7–15, 1998.

    Article  Google Scholar 

  • P. Smith. Explaining Chaos. Cambridge University Press, Cambridge, 1998.

    Book  Google Scholar 

  • M. Suarez. Fictionals, conditionals and stellar astrophysics. International Studies in the Philosophie of Science, 27: 235–252, 2013.

    Article  Google Scholar 

  • A. A. Tsonis. Chaos: From Theory to Applications. Plenum Press, New York, 1992.

    Book  Google Scholar 

  • A. A. Tsonis and J. B. Elsner. Chaos, Strange attractors and weather. Bulletin of the American Meteorological Society, 70: 14–23, 1989.

    Article  Google Scholar 

  • W. Tucker. A rigorous ODE solver and Smale’s 14th problem. Foundations of Computational Mathematics, 2: 53–117, 2002.

    Article  Google Scholar 

  • M. Viana. What’s new on Lorenz strange attractors. The Mathematical Intelligencer, 22: 6–18, 2000.

    Article  Google Scholar 

  • C. Werndl. Justifying definitions in mathematics: Going beyond Lakatos. Philosophia Mathematica, 17: 313–340, 2009c.

    Article  Google Scholar 

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Zuchowski, L.C. (2017). Evaluation of Chaotic Models. In: A Philosophical Analysis of Chaos Theory. New Directions in the Philosophy of Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-54663-6_4

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