Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors

Ulrike Feudel, Celso Grebogi, Leon Poon, James A. Yorke

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

We study a simple mechanical system consisting of two rotors that possesses a large number (3000+) of coexisting periodic attractors. A complex fractal boundary separates these tiny islands of stability and their basins of attraction. Hence, the system's long term behavior is acutely sensitive to the initial conditions. This sensitivity combined with the system's many periodic sinks give rise to a rich dynamical behavior when the system is subjected to small amplitude noise. This dynamical behavior is of great utility, and this is demonstrated by using perturbations which are smaller than the noise level to gear and influence the dynamics toward a specific periodic behavior. (C) 1998 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)171-180
Number of pages10
JournalChaos, Solitons & Fractals
Volume9
Issue number1-2
DOIs
Publication statusPublished - 1998

Keywords

  • transverse laser patterns
  • multiple steady-states
  • semiconductor superlattices
  • multistability
  • networks
  • model
  • chaos

Cite this

Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors. / Feudel, Ulrike; Grebogi, Celso; Poon, Leon; Yorke, James A.

In: Chaos, Solitons & Fractals, Vol. 9, No. 1-2, 1998, p. 171-180.

Research output: Contribution to journalArticle

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AB - We study a simple mechanical system consisting of two rotors that possesses a large number (3000+) of coexisting periodic attractors. A complex fractal boundary separates these tiny islands of stability and their basins of attraction. Hence, the system's long term behavior is acutely sensitive to the initial conditions. This sensitivity combined with the system's many periodic sinks give rise to a rich dynamical behavior when the system is subjected to small amplitude noise. This dynamical behavior is of great utility, and this is demonstrated by using perturbations which are smaller than the noise level to gear and influence the dynamics toward a specific periodic behavior. (C) 1998 Elsevier Science Ltd. All rights reserved.

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KW - multistability

KW - networks

KW - model

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