Dynamics with Delays and Expectations

  • Alexander S. Mikhailov
  • Vera Calenbuhr
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

All living beings are on a road that starts with their birth and ends with their death. The coordinate along this road is the age of a biological organism. A population typically consists of individuals of various ages that collaborate or compete each with another. The characteristic property of such interactions is that they are nonlocal and that individuals of largely different ages can interact. The distribution over ages, representing the demographic structure of a population, evolves with time and may show complex temporal behavior.

Keywords

Europe Leukemia Respiration Expense Eter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 244.
    R. May, Nature 261, 459 (1976)ADSCrossRefGoogle Scholar
  2. 245.
    A.S. Mikhailov, A.Yu. Loskutov, Foundations of Synergetics II. Chaos and Noise, 2nd revised edn. (Springer, Berlin 1991, 1996)CrossRefGoogle Scholar
  3. 246.
    M.C. Mackey, L. Glass, Science 197, 287 (1977)ADSCrossRefGoogle Scholar
  4. 247.
    L. Glass, M.C. Mackey, Ann. New York Acad. Sci. 316, 214 (1979)ADSCrossRefGoogle Scholar
  5. 248.
    M.C. Mackey, U. An Der Heiden, Funk. Biol. Med. 1, 156 (1982)Google Scholar
  6. 249.
    M.C. Mackey, J.G. Milton, Ann. New York Acad. Sci. 504, 16 (1988)ADSCrossRefGoogle Scholar
  7. 250.
    G. Benchetrit, P. Baconnier, J. Demongeot (eds.), Concepts and Formalizations in the Control of Breathing (Manchester University Press, Manchester 1987)Google Scholar
  8. 251.
    L. Rensing, U. An Der Heiden, M.C. Mackey (eds.), Temporal Disorder in Human Osillatory Systems (Springer, Berlin, Heidelberg, New York 1987)Google Scholar
  9. 252.
    C. Haurie, D.C. Dale, M.C. Mackey, Blood 92, 2629 (1998)Google Scholar
  10. 253.
    K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980)ADSCrossRefGoogle Scholar
  11. 254.
    P. Nardone, P. Mandel, R. Kapral, Phys. Rev. A 33, 2465 (1986)ADSCrossRefGoogle Scholar
  12. 255.
    N. Khrustova, G. Veser, A.S. Mikhailov, R. Imbihl, Phys. Rev. Lett. 75, 3564 (1995)ADSCrossRefGoogle Scholar
  13. 256.
    N. Khrustova, A.S. Mikhailov, R. Imbihl, J. Chem. Phys. 107, 2096 (1997)ADSCrossRefGoogle Scholar
  14. 257.
    J.-M. Grandmont, P. Malgrange, J. Econ. Th. 40, 3 (1986)MathSciNetCrossRefGoogle Scholar
  15. 258.
    R. Deneckere, S. Pelikan, J. Econ. Th. 40, 13 (1986)MathSciNetMATHCrossRefGoogle Scholar
  16. 259.
    M. Boldrin, L. Montrucchio, J. Econ. Th. 40, 26 (1986)MathSciNetMATHCrossRefGoogle Scholar
  17. 260.
    R.A. Dana, L. Montrucchio, J. Econ. Th. 40, 40 (1986)MathSciNetMATHCrossRefGoogle Scholar
  18. 261.
    J.-M. Grandmont, G. Laroque, J. Econ. Th. 40, 138 (1986)MathSciNetMATHCrossRefGoogle Scholar
  19. 262.
    K. Shell, Citedin J.-M. Grandmont, P. Malgrange, J. Econ. Th. 40, 3 (1986)CrossRefGoogle Scholar
  20. 263.
    D. Cass, K. Shell, J. Polit. Econ. 91, 193 (1983)CrossRefGoogle Scholar
  21. 264.
    C. Azariadis, J. Econ. Th. 25, 380 (1981)MATHCrossRefGoogle Scholar
  22. 265.
    C. Azariadis, R. Guesnerie, “Sunspots and Cycles” . CARESS Working Paper 8322R, University of Pennsylvania (1983; revised 1984)Google Scholar
  23. 266.
    R. Guesnerie, J. Econ Th. 40, 103 (1986)MathSciNetMATHCrossRefGoogle Scholar
  24. 267.
    R.H. Day, W. Huang, J. Econ. Beh. Org. 14, 299 (1990)CrossRefGoogle Scholar
  25. 268.
    V.L. Smith, G.L. Suchanek, A.W. Williams, Econometrica 5, 1119 (1988)CrossRefGoogle Scholar
  26. 269.
    P. Anderson, K.J. Arrow, D. Pines (eds.), The Economy as an Evolving Complex System (Addison-Wesley, Reading, MA 1988)MATHGoogle Scholar
  27. 270.
    W.B. Arthur, S.N. Durlauf, D.A. Lane (eds.), The Economy as an Evolving Complex System II (Addison-Wesley, Reading, MA 1997)Google Scholar
  28. 271.
    W.B. Arthur, Am. Econ. Rev. 84, 406 (1994)Google Scholar
  29. 272.
    W.B. Arthur, Complexity 1, 20 (1995)MATHGoogle Scholar
  30. 273.
    W.B. Arthur, J.H. Holland, B. LeBaron, R. Palmer, P. Taylor, In W.B. Arthur, S.N. Durlauf, D.A. Lane (eds.), The Economy as an Evolving Complex System II (Addison-Wesley, Reading, MA 1997), p. 15Google Scholar
  31. 274.
    R. Axelrod, W.D. Hamilton, Science 211, 1390 (1981)MathSciNetADSMATHCrossRefGoogle Scholar
  32. 275.
    R. Axelrod, The Evolution of Cooperation (Basic Books/Harper Collins, New York 1984)Google Scholar
  33. 276.
    R. Axelrod, D. Dion, Science 242, 1385 (1988)ADSCrossRefGoogle Scholar
  34. 277.
    N.S. Glance, B.A. Huberman, J. Math. Soc. 17, 281 (1993)MATHCrossRefGoogle Scholar
  35. 278.
    N.S. Glance, B.A. Huberman, Phys. Lett. A 165, 432 (1992)ADSCrossRefGoogle Scholar
  36. 279.
    B.A. Huberman, N.S. Glance, In Modelling Rational and Moral Agents, ed. P. Danielson (Oxford University Press, Oxford 1996), p. 210Google Scholar
  37. 280.
    B.B. Mandelbrot, J. Business 36, 394 (1963)CrossRefGoogle Scholar
  38. 281.
    R.N. Mantegna, Physica A 179, 232 (1991)ADSCrossRefGoogle Scholar
  39. 282.
    R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)ADSCrossRefGoogle Scholar
  40. 283.
    J.-P. Bouchaud, Physica A 263, 415 (1999)MathSciNetADSCrossRefGoogle Scholar
  41. 284.
    L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters, Phys. Rev. Lett. 83, 1467 (1999)ADSCrossRefGoogle Scholar
  42. 285.
    V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley, Phys. Rev. Lett. 83, 1471 (1999)ADSCrossRefGoogle Scholar
  43. 286.
    J.-P. Bouchaud, M. Potters, Theorie des Risques Financiéres (Alea-Sacley, Eyrolles 1997), English translation in preparationGoogle Scholar
  44. 287.
    R.N. Mantegna, H.E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge 1999)CrossRefGoogle Scholar
  45. 288.
    H. Takayasu, H. Miura, T. Hirabayashi, K. Hamada, Physica A 184, 127 (1992)ADSCrossRefGoogle Scholar
  46. 289.
    M. Levy, S. Solomon, Int. J. Mod. Phys. C 7, 595 (1996)ADSCrossRefGoogle Scholar
  47. 290.
    G. Caldarelli, M. Marsili, Y.-C. Zhang, Europhys. Lett. 40, 479 (1997)ADSCrossRefGoogle Scholar
  48. 291.
    A.-H. Sato, H. Takayasu, Physica A 250, 231 (1998)MATHCrossRefGoogle Scholar
  49. 292.
    J.-P. Bouchaud, R. Cont, Eur. Phys. J. B 6, 543 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
  • Vera Calenbuhr
    • 2
  1. 1.Fritz-Haber-InstitutMax-Planck-GesellschaftBerlinGermany
  2. 2.Joint Research CenterDirectorate for Science Strategy European CommissionBrusselsBelgium

Personalised recommendations