### 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 language | English |
---|---|

Pages (from-to) | 71-81 |

Number of pages | 11 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 54 |

Issue number | 1 |

Publication status | Published - Jul 1996 |

### Keywords

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

### Cite this

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

*54*(1), 71-81.

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

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 54, no. 1, pp. 71-81.

}

TY - JOUR

T1 - Map with more than 100 coexisting low-period periodic attractors

AU - Feudel, U

AU - Grebogi, C

AU - Hunt, B R

AU - Yorke, J A

PY - 1996/7

Y1 - 1996/7

N2 - 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.

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.

KW - DISSIPATIVE STANDARD MAP

KW - BASIN BOUNDARIES

KW - SYSTEMS

KW - TRANSITION

KW - SINKS

KW - CHAOS

KW - SETS

M3 - Article

VL - 54

SP - 71

EP - 81

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

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

SN - 1063-651X

IS - 1

ER -