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Implications of a continuous approach to chaotic modeling

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 945))

Abstract

Application of chaos theory to medicine has yielded intriguing and controversial results. In this paper, a continuous conjecture for the solution of the Poincaré equation suggests that chaos provides a framework for the measurement of disorder within a system. However, as demonstrated by the behavior of the continuous versus the discrete approach to chaos, the general use of the term chaos must be used with care. The theoretical results are illustrated in two medical applications dealing with hemodynamic flow and congestive heart failure.

This work was supported in part by a grant from University of California Valley Medical Education Foundation.

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References

  1. Poincaré. H., Memoire sur les courbes definies par les equations differentielles, J. Math. Pures et Appliq., 4th Ser., 1, 1885, 167–244.

    Google Scholar 

  2. Gleick, J., Chaos, Making a New Science, Penguin Books, New York, 1987.

    Google Scholar 

  3. Cohen, M.E., Hudson, D.L., Anderson, M.F., A conjectured continuous approach to chaotic modeling, Nonlinear Theory and Its Applications, 1993, 783–786.

    Google Scholar 

  4. Tsonis, P.A. Tsonis, A.A., Chaos: principles and implications in biology, Computer Applications in the Biosciences, 5 (1), 1989, 27–32.

    Google Scholar 

  5. Goldberger, A.L., West, B.J., Fractals in physiology and medicine, Yale Journal of Biology and Medicine, 60, 1987, 421–435.

    Google Scholar 

  6. Goldberger, A.L., Cardiac chaos, Science, 243 (2987), 1989, 1419.

    Google Scholar 

  7. Cohen, M.E., Hudson, D.L., Computational Aspects of Chaos Theory, ISCA, 1994, 89–93.

    Google Scholar 

  8. Cohen, M.E., Hudson, D.L., Anderson, M.F., The effect of vasoactive drugs on the chaotic nature of blood flow, MEDINFO, K.C. Lun, et al., Eds., North Holland, 1992, 931–936.

    Google Scholar 

  9. Szego, G., Orthogonal Polynomials, American Math. Soc. Colloquium Publications, XXIII, 1939, 59.

    Google Scholar 

  10. Burton, R.L., Faires, J.D., Reynolds, A.C., Numerical Analysis, Prindle, Weber, and Schmidt, Boston, 1978.

    Google Scholar 

  11. Cohen, M.E., Hudson, D.L., Moazamipour, H., Anderson, M.F., Chaotic blood flow analysis in an animal model, Computer Applications in Medical Care, 1990, 14, 323–327.

    Google Scholar 

  12. Cohen, M.E., Hudson, D.L., Anderson, M.F., Vazquez, C., Blood flow data exhibit chaotic properties, Int. J. of Microcomputer Applications, 12 (3), 1993, 82–87.

    Google Scholar 

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Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1995 Springer-Verlag Berlin Heidelberg

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Cohen, M.E., Hudson, D.L., Anderson, M.F., Deedwania, P.C. (1995). Implications of a continuous approach to chaotic modeling. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035980

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  • DOI: https://doi.org/10.1007/BFb0035980

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60116-6

  • Online ISBN: 978-3-540-49443-0

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