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Self-Similar Basin Boundary in a Continuous System

  • O. E. Rossler
  • J. L. Hudson
  • M. Klein
  • C. Mira
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A four-variable ordinary differential equation with hyperchaos is investigated further numerically. A self-similar Sierpinski-type fractal is found in a plane of initial conditions if the prospective fate of each point (whether it escapes through the one or the other escape hole in the exploded hyperchaotic attractor) is used for a coloring criterion. A basin boundary of the same qualitative shape therefore exists in either this equation or a closely related one. All hyper-chaotic systems are eligible for an analogous investigation — both numerically and, if possible, experimentally.

Keywords

Chaotic Attractor Stable Manifold Basin Boundary Slow Manifold Hyperchaotic 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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Copyright information

© Springer-Verlags Berlin Heidelberg 1990

Authors and Affiliations

  • O. E. Rossler
    • 1
  • J. L. Hudson
    • 2
  • M. Klein
    • 1
  • C. Mira
    • 3
  1. 1.Institute for Physical and Theoretical ChemistryU. of TubingenTubingenGermany
  2. 2.Department of Chemical EngineeringUniversity of VirginiaCharlottesvilleUSA
  3. 3.Systèmes Nonlinéaires et ApplicationsINSA of ToulouseToulouse CedexFrance

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