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Preturbulence, Strange Attractors and Geometric Models

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Part of the Applied Mathematical Sciences book series (AMS,volume 41)

Abstract

We commence our study of the parameter region r > 13.926 by attempting to confirm the first of the two suggestions made at the end of the last chapter. We can use the computer to locate stable and non-stable periodic orbits. The techniques used are based on Newton1s method, are well known, and are described in Appendix E. To use the techniques it is necessary to have a reasonably good guess for the position and period of the orbit we wish to locate. Appendix E contains practical hints on how to come by such initial guesses, and on how to use the techniques. Appendix E also contains the description of a technique for following a periodic orbit with changing parameter.

Keywords

  • Periodic Orbit
  • Hopf Bifurcation
  • Unstable Manifold
  • Homoclinic Orbit
  • Stable Manifold

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.

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© 1982 Springer-Verlag New York Inc.

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Sparrow, C. (1982). Preturbulence, Strange Attractors and Geometric Models. In: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Applied Mathematical Sciences, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5767-7_3

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  • DOI: https://doi.org/10.1007/978-1-4612-5767-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90775-8

  • Online ISBN: 978-1-4612-5767-7

  • eBook Packages: Springer Book Archive