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Communications in Mathematical Physics

, Volume 67, Issue 2, pp 93–108 | Cite as

Preturbulence: A regime observed in a fluid flow model of Lorenz

  • James L. Kaplan
  • James A. Yorke
Article

Abstract

This paper studies a forced, dissipative system of three ordinary differential equations. The behavior of this system, first studied by Lorenz, has been interpreted as providing a mathematical mechanism for understanding turbulence. It is demonstrated that prior to the onset of chaotic behavior there exists a preturbulent state where turbulent orbits exist but represent a set of measure zero of initial conditions. The methodology of the paper is to postulate the short term behavior of the system, as observed numerically, to establish rigorously the behavior of particular orbits for all future time. Chaotic behavior first occurs when a parameter exceeds some critical value which is the first value for which the system possesses a homoclinic orbit. The arguments are similar to Smale's “horseshoe”.

Keywords

Differential Equation Neural Network Statistical Physic Complex System Fluid Flow 
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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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • James L. Kaplan
    • 1
  • James A. Yorke
    • 2
  1. 1.Department of MathematicsBoston UniversityBostonUSA
  2. 2.Institute for Physical Science and Technology and Department of MathematicsUniversity of MarylandCollege ParkUSA

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