• To provide a brief historical introduction to chaos control.

  • To introduce two methods of chaos control for one-and two-dimensional discrete maps.


Control Region Chaotic System Chaotic Attractor Plot Time Series Unstable Periodic Orbit 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Recommended Reading

  1. 1.
    T. Kapitaniak, Chaos for Engineers: Theory, Applications and Control, 2nd ed., Springer-Verlag, New York, 2000.CrossRefGoogle Scholar
  2. 2.
    S. Lynch and A. L. Steele, Controlling chaos in nonlinear bistable optical resonators, Chaos Solitons Fractals, 11-5 (2000), 721–728.CrossRefGoogle Scholar
  3. 3.
    M. Buchanan, Fascinating rhythm, New Scientist, 3 January (1998), 20–25.Google Scholar
  4. 4.
    N. P. Chau, Controlling chaos by periodic proportional pulses, Phys. Lett. A, 234 (1997), 193–197.CrossRefGoogle Scholar
  5. 5.
    T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics, Academic Press, New York, 1996.MATHGoogle Scholar
  6. 6.
    A. Garfinkel, M. L. Spano, W. L. Ditto, and J. N. Weiss, Controlling cardiac chaos, Science, 257 (1992), 1230–1235.CrossRefGoogle Scholar
  7. 7.
    R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, and E. R. Hunt, Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system, Phys. Rev. Lett., 68 (1992), 1259–1262.CrossRefGoogle Scholar
  8. 8.
    E. R. Hunt, Stabilizing high-period orbits in a chaotic system: The diode resonator, Phys. Rev. Lett., 67 (1991), 1953–1955.CrossRefGoogle Scholar
  9. 9.
    J. Singer, Y.-Z. Wang, and H. H. Bau, Controlling a chaotic system, Phys. Rev. Lett., 66 (1991), 1123–1125.CrossRefGoogle Scholar
  10. 10.
    W. L. Ditto, S. N. Rausseo, and M. L. Spano, Experimental control of chaos. Phys. Rev. Lett., 65 (1990), 3211–3214.CrossRefGoogle Scholar
  11. 11.
    T. Shinbrot, C. Grebogi, E. Ott, and J. A. Yorke, Using chaos to direct trajectories to targets, Phys. Rev. Lett., 65 (1990), 3215–3218.CrossRefGoogle Scholar
  12. 12.
    L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821–824.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    E. Ott, C. Grebogi, and J. A. Yorke, Controlling chaos, Phys. Rev. Lett., 64 (1990), 1196–1199.MathSciNetCrossRefMATHGoogle 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

Personalised recommendations