Map with more than 100 coexisting low-period periodic attractors

U Feudel, C Grebogi, B R Hunt, J A Yorke

Research output: Contribution to journalArticle

131 Citations (Scopus)

Abstract

We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enough. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to be detected. We expect the complexity described here to be even more pronounced for higher-dimensional systems, like the double rotor, for which we find more than 1000 coexisting low-period periodic attractors.

Original languageEnglish
Pages (from-to)71-81
Number of pages11
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume54
Issue number1
Publication statusPublished - Jul 1996

Keywords

  • DISSIPATIVE STANDARD MAP
  • BASIN BOUNDARIES
  • SYSTEMS
  • TRANSITION
  • SINKS
  • CHAOS
  • SETS

Cite this

Map with more than 100 coexisting low-period periodic attractors. / Feudel, U ; Grebogi, C ; Hunt, B R ; Yorke, J A .

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 54, No. 1, 07.1996, p. 71-81.

Research output: Contribution to journalArticle

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AB - We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enough. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to be detected. We expect the complexity described here to be even more pronounced for higher-dimensional systems, like the double rotor, for which we find more than 1000 coexisting low-period periodic attractors.

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KW - TRANSITION

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KW - CHAOS

KW - SETS

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JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

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