Nonlinear Discrete Dynamical Systems

  • Stephen Lynch


  • To introduce nonlinear one-and two-dimensional iterated maps.

  • To investigate period-doubling bifurcations to chaos.

  • To introduce the notion of universality.


Periodic Orbit Lyapunov Exponent Bifurcation Diagram Periodic Point Chaotic Attractor 
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Recommended Reading

  1. 1.
    E. Ahmed, A. El-Misiery, and H. N. Agiza, On controlling chaos in an inflation-unemployment dynamical system, Chaos Solitons Fractals, 109 (1999), 1567-1570.MathSciNetCrossRefGoogle Scholar
  2. 2.
    F. Pasemann and N. Stollenwerk, Attractor switching by neural control of chaotic neurodynamics, Comput. Neural Systems, 9 (1998), 549-561.CrossRefMATHGoogle Scholar
  3. 3.
    H. Nagashima and Y. Baba, Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena, Institute of Physics, Bristol, PA, 1998.Google Scholar
  4. 4.
    R. A. Holmgrem, A First Course in Discrete Dynamical Systems, Springer-Verlag, New York, 1996.CrossRefGoogle Scholar
  5. 5.
    D. Kaplan and L. Glass, Understanding Nonlinear Dynamics, Springer-Verlag, New York, 1995.CrossRefMATHGoogle Scholar
  6. 6.
    S. M. Hammel, C. K. R. T. Jones, and J. V. Maloney, Global dynamical behavior of the optical field in a ring cavity, J. Optim. Soc. Amer. B, 2 (1985), 552-564.CrossRefGoogle Scholar
  7. 7.
    R. H. Day, Irregular growth cycles, Amer. Econ. Rev., 72 (1982), 406-414.Google Scholar
  8. 8.
    A. Lasota, Ergodic problems in biology, Astérisque, 50 (1977), 239-250.MathSciNetGoogle Scholar
  9. 9.
    T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, 82 (1975), 985-992.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1974.Google Scholar
  11. 11.
    M. Hénon, Numerical study of quadratic area-preserving mappings, Quart. Appl. Math., 27 (1969), 291-311.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Stephen Lynch
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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