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Exploring Nature’s Roulette Wheel: Chaos in Biological Systems

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Cell to Cell Signals in Plants and Animals

Part of the book series: NATO ASI Series ((ASIH,volume 51))

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Abstract

Chaos is irregular, unpredictable behaviour generated by a simple, nonlinear deterministic system; the paradoxical combination of unpredictability (in the long term) with simple determinism results from sensitivity to initial conditions. Turbulent irregularity dominates macroscopic physical phenomena, from laboratory to galactic physics, and the current enthusiasm for chaotic dynamics [14, 44] follows from the discovery of universality in chaos [7].

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References

  1. Aguda, B. and Larter, R. J. Chem. Phys. (1989).

    Google Scholar 

  2. Aron, J.L and Schwartz, I.B. J. Theor. Biol. 112: 403 (1985).

    Article  Google Scholar 

  3. Boiteux, A. and Hess, B. Phil. trans. Royal Soc. B293:5 (1981).

    Article  Google Scholar 

  4. Brindley, J., Kaas-Petersen, C. and Spence, A. Physica-D 34: 456 (1989).

    Article  Google Scholar 

  5. Christiansen, P.L. and Parmentier, R.D. Structure, coherence and chaos in dynamical systems. Manchester University Press 1989.

    Google Scholar 

  6. Conrad, M. in [9].

    Google Scholar 

  7. Cvitanovic, P. (ed.) Universality in Chaos Adam Hilger, Bristol 1985.

    Google Scholar 

  8. Davydov, A.S. Biology and quantum mechanics. Pergamon, Oxford (1982).

    Google Scholar 

  9. Degn, H., Holden, A.V. and Olsen, L.F. (eds.) Chaos in Biological Systems, Plenum, New York, 1988.

    Google Scholar 

  10. Degn, H. and Mayer, D. Biochem Biophys. Acta 180: 291 (1969).

    Article  PubMed  CAS  Google Scholar 

  11. Durston, A.J. Devel. Biol. 38: 308 (1974).

    Article  CAS  Google Scholar 

  12. Elton, C. and Nicholson, M.J. J. Animal Ecol. 11:96(1942).

    Article  Google Scholar 

  13. Glass, L. and Mackey, M.C. Annals N.Y. Acad. Sci. 316: 214 (1979).

    Article  CAS  Google Scholar 

  14. Gleick, J. Chaos: making of a new science Heinemann, London 1988.

    Google Scholar 

  15. Grassberger, P. Nature (London) 323: 609 (1986).

    Article  Google Scholar 

  16. Grassberger, P. and Procaccia, I. Physica-D 9:189 (1983).

    Article  Google Scholar 

  17. Hassel, M.P., Lawton, J.H. and May, R.M. J. Animal Ecol. 45: 471 (1976).

    Article  Google Scholar 

  18. Hess, B. and Markus, M. Trends Biochem. Sci., 12:45 (1987).

    Article  CAS  Google Scholar 

  19. Hodgkin, A.L. and Huxley, A.F. J. Physiol (London) 117: 500 (1952).

    CAS  Google Scholar 

  20. Holden, A.V. The mathematics of excitation. In Biomathematics in 1980, ed. L.M. Ricciardi and A.C. Scott. North-Holland, Amsterdam (1982).

    Google Scholar 

  21. Holden, A.V. (ed.). Chaos. Manchester University Press, Manchester, 1986; Princeton University Press, Princeton, New Jersey, 1986.

    Google Scholar 

  22. Holden, A.V., Markus, M. and Othmer, H. (eds.) Nonlinear wave processes in excitable media. Plenum, New York, 1990.

    Google Scholar 

  23. Irisawa, H. and Noma, A. In Cardiac Rate and Rhythm ed. L.N. Bouman and H.J. Jongsma. Martinus Nijoff, The Hague p. 35 (1982).

    Chapter  Google Scholar 

  24. Kot, M. (in preparation).

    Google Scholar 

  25. Li, Y.-T. and Yorke, J. Am. Math. Monthly, 82: 985 (1975).

    Article  Google Scholar 

  26. Markus, M., Kuschmitz, D. and Hess, B. FRBS Lett. 172: 235 (1984).

    Article  CAS  Google Scholar 

  27. May, R.M. Nature (London) 261: 459 (1976).

    Article  CAS  Google Scholar 

  28. May, R.M. Proc. Royal Soc. Lond. A413: 27 (1987).

    Article  Google Scholar 

  29. Olsen, L.F. Phys. Lett 94A: 454 (1983).

    CAS  Google Scholar 

  30. Olsen L.F. and Degn, H. Nature 267:177 (1977).

    Article  PubMed  CAS  Google Scholar 

  31. Olsen, L.F. and Degn, H. Q. Rev. Biophys. 18: 165 (1985).

    Article  CAS  Google Scholar 

  32. Pool, R. Science 243: 25 (1989).

    Article  PubMed  CAS  Google Scholar 

  33. Pool, R. Science 243: 310 (1989).

    Article  PubMed  CAS  Google Scholar 

  34. Pool, R. Science 243: 604 (1989).

    Article  PubMed  CAS  Google Scholar 

  35. Rapp, P. J. Exp. Biol. 81: 281 (1979).

    PubMed  CAS  Google Scholar 

  36. Rogers, T.D. Prog. Theor. Biol. 6: 91 (1981).

    Google Scholar 

  37. Ross, J. and Schell, M. Ann. Rev. Biophys. Biophys. Chem. 16: 401 (1987).

    Article  CAS  Google Scholar 

  38. Schaffer, W.M. Am. Nat. 124: 798 (1984).

    Article  Google Scholar 

  39. Schaffer, W.M. IMA J. Math. Appl. Med. & Biol. 2: 221 (1985).

    Article  CAS  Google Scholar 

  40. Schaffer, W. M., and Kot, M. J. Theor. Biol 112: 403 (1985).

    Article  PubMed  CAS  Google Scholar 

  41. Schaffer, W.M., Ellner, S.E. and Kot, M. J. Math. Biol. 24: 479 (1986).

    Article  CAS  Google Scholar 

  42. Schaffer, W.M., Olsen, L.F., Truty, G.L. and Fulmer, S.L. Proc. AAAS Annual meeting, San Francisco 1989, in press.

    Google Scholar 

  43. Sporns, O., Roth, S. and Seeliog, F.F. Physica-D 26: 215 (1987).

    Article  Google Scholar 

  44. Stewart, I. Does God Play dice? The mathematics of chaos. Blackwell, Oxford 1989.

    Google Scholar 

  45. Takens, F. Lect. Notes Math. 898: 366 (1981).

    Article  Google Scholar 

  46. Tomita, K. Phys. Rep. 86:113 (1982).

    Article  Google Scholar 

  47. Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, JA Physica-D 16: 285 (1985).

    Article  Google Scholar 

  48. Wolfram, S Physica-D 10:1 (1984).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Nonlinear Studies, The University, Leeds, LS2 9JT, UK

    Arun V. Holden & Lars Folke Olsen

  2. Department of Biochemistry, Odense University, Odense, Denmark

    Arun V. Holden & Lars Folke Olsen

Authors
  1. Arun V. Holden
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  2. Lars Folke Olsen
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Editor information

Editors and Affiliations

  1. MPI für Experimentelle Medizin, Hermann Rein Str. 3, 3400, Göttingen, Germany

    Volker Neuhoff

  2. School of Life Sciences Dept. of Biology, University of Hull, Hull, HU6 7RX, England

    John Friend

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© 1991 Springer-Verlag Berlin Heidelberg

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Holden, A.V., Olsen, L.F. (1991). Exploring Nature’s Roulette Wheel: Chaos in Biological Systems. In: Neuhoff, V., Friend, J. (eds) Cell to Cell Signals in Plants and Animals. NATO ASI Series, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76470-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-76470-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76472-1

  • Online ISBN: 978-3-642-76470-7

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