Advertisement

Three-Dimensional Autonomous Systems and Chaos

  • Stephen Lynch

Abstract

  • To introduce first-order ODEs in three variables.

  • To discuss chaos in more depth.

Keywords

Lyapunov Exponent Rayleigh Number Phase Portrait Unstable Manifold Chaotic Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Recommended Reading

  1. 1.
    G A. Gottwald and I. Melbourne, A new test for chaos in deterministic systems, Proc. Roy. Soc. London Set: A, 460-2042 (2004), 603-611.Google Scholar
  2. 2.
    S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed., Texts in Applied Mathematics 2, Springer-Verlag, New York, 2003.Google Scholar
  3. 3.
    J. Borresen and S. Lynch. Further investigation of hysteresis in Chua’s circuit, Internat. .J. Bifurcation Chaos, 12 (2002), 129-134.Google Scholar
  4. 4.
    R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd ed., Oxford University Press, London, 2000.CrossRefGoogle Scholar
  5. 5.
    M. Zoltowski, An adaptive reconstruction of chaotic attractors out of their single trajectories, Signal Process., 80-6 (2000), 1099-1113.CrossRefGoogle Scholar
  6. 6.
    N. Arnold, Chemical Chaos, Hippo, London, 1997.Google Scholar
  7. 7.
    S. K. Scott, Oscillations, Waves, and Chaos in Chemical Kinetics, Oxford Science Publications, Oxford, UK, 1994.Google Scholar
  8. 8.
    R. N. Madan, Chua’s Circuit: A Paradigm for Chaos, World Scientific, Singapore, 1993.MATHGoogle Scholar
  9. 9.
    K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Progr. Theoret. Phys., 83-5 (1990), 875-893.MathSciNetCrossRefGoogle Scholar
  10. 10.
    J. P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Lyapunov exponents from time series, Phys. Rev. A, 34-6 (1986), 4971-4979.MathSciNetCrossRefGoogle Scholar
  11. 11.
    R. Field and M. Burger, eds., Oscillations and Travelling Waves in Chemical Systems, Wiley, New York, 1985.Google Scholar
  12. 12.
    C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer-Verlag, New York, 1982.Google Scholar
  13. 13.
    O. E. Rössler, An equation for continuous chaos, Phys. Lett., 57-A (1976), 397-398.Google Scholar
  14. 14.
    E. N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci., 20 (1963), 130-141.CrossRefGoogle 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