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Introduction and Simple Properties

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

Abstract

In 1963 E. N. Lorenz wrote a remarkable paper. In it he described a three parameter family of three-dimensional ordinary differential equations which appeared, when integrated numerically on a computer, to have extremely complicated solutions. These equations, now known as the Lorenz equations, have been studied by many authors in the years since 1963 and one of our aims, in these notes, is to contribute to this study. It is necessary, therefore, to explain some of the reasons why the equations generated so much interest initially and why they warrant further study.

Keywords

  • Periodic Orbit
  • Chaotic System
  • Rayleigh Number
  • Hopf Bifurcation
  • Lorenz System

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). Introduction and Simple Properties. 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_1

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  • DOI: https://doi.org/10.1007/978-1-4612-5767-7_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90775-8

  • Online ISBN: 978-1-4612-5767-7

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