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.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
R. W. Batterman. Defining chaos. Philosophy of Science, 60: 43–66, 1993.
A. Bokulich. Horizontal models: From bakers to cats. Philosophy of Science, 70:609–627, 2003.
N. Chernov and R. Markarian. Chaotic Billiards. American Mathematical Society, New York, 2006.
J. M. Cushing. Integrodifferential Equations and Delay Models in Population Dynamics. Springer, Berlin, 1977.
P. Cvitanovic. Universality in Chaos. Adam Hilger, Bristol, 1986.
R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison Wesley, Redwood City, 1989.
J. Guckenheimer, G. Oster, and A. Ipaktchi. The dynamics of density dependent population models. Journal of Mathematical Biology, 4: 101–147, 1977.
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.
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.
M. W. Hirsch, S. Smale, and R. L. Devaney. Differential Equations, Dynamical Systems and An Introduction to Chaos. Elsevier, Amsterdam, 2004.
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.
S. H. Kellert. In the Wake of Chaos. The University of Chicago Press, Chicago, 1993.
J. Koperski. Models, confirmation and chaos. Philosophy of Science, 65: 624–649, 1998.
M. Kot and W. M. Schaffer. Discrete-time growth-dispersal models. Mathematical Biosciences, 80: 109–136, 1986.
T.-Y. Li and J. A. Yorke. Period three implies chaos. The American Mathematical Monthly, 82: 985–992, 1975.
E. Lorenz. The Essence of Chaos. UCL Press, London, 1993.
R. M. May. Biological populations with non-overlapping generations: Stable points, stable Cycles, and chaos. Science, 15: 645–647, 1974.
R. M. May. Simple mathematical models with very complicated dynamics. Nature, 261: 459–467, 1976.
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.
R. M. May and G. F. Osler. Bifurcations and dynamic complexity in simple ecological models. The American Naturalist, 110: 573–599, 1976.
Mark McEvoy. Experimental mathematics, computers and the a priori. Synthese, 190: 397–412, 2013.
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.
K. Palmer. Shadowing in Dynamical Systems: Theory and Application. Springer, Boston, 2000.
R. Pool. Is it chaos, or is it just noise? Science, 243: 25–28, 1989.
R. Robertson and A. Combs. Chaos Theory in Psychology and the Life Sciences. Lawrence Erlbaum, Hove, 1995.
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.
S. Smale. Differentially dynamical systems. i. diffeomorphisms. Bulletin of the American Mathematical Society, 73: 747–816, 1967.
S. Smale. Mathematical problems for the new century. The Mathematical Intelligencer, 20: 7–15, 1998.
P. Smith. Explaining Chaos. Cambridge University Press, Cambridge, 1998.
M. Suarez. Fictionals, conditionals and stellar astrophysics. International Studies in the Philosophie of Science, 27: 235–252, 2013.
A. A. Tsonis. Chaos: From Theory to Applications. Plenum Press, New York, 1992.
A. A. Tsonis and J. B. Elsner. Chaos, Strange attractors and weather. Bulletin of the American Meteorological Society, 70: 14–23, 1989.
W. Tucker. A rigorous ODE solver and Smale’s 14th problem. Foundations of Computational Mathematics, 2: 53–117, 2002.
M. Viana. What’s new on Lorenz strange attractors. The Mathematical Intelligencer, 22: 6–18, 2000.
C. Werndl. Justifying definitions in mathematics: Going beyond Lakatos. Philosophia Mathematica, 17: 313–340, 2009c.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-54663-6_4
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-319-54662-9
Online ISBN: 978-3-319-54663-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)