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Applied Mathematical Sciences

The Lorenz Equations

Bifurcations, Chaos, and Strange Attractors

Authors: Sparrow, Colin

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The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be­ tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be­ tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-1-4612-5767-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.99
price for USA in USD
  • ISBN 978-0-387-90775-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Lorenz Equations
Book Subtitle
Bifurcations, Chaos, and Strange Attractors
Authors
Series Title
Applied Mathematical Sciences
Series Volume
41
Copyright
1982
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4612-5767-7
DOI
10.1007/978-1-4612-5767-7
Softcover ISBN
978-0-387-90775-8
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XII, 270
Topics