### Abstract

Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, is

uncovered in the six dimensional Poincare map of a symmetric three-degree of freedom vibroimpact

system. Accompanied by symmetry restoring bifurcation, this QC is the consequence of a

novel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The six

dimensional Poincare map P is the 2-fold composition of another virtual implicit map Q, yielding

the symmetry of the system. Map Q can capture two conjugate attractors, which is at the core of

the dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzed

in detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittency

induced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenly

embedded in a chaotic one, QC is induced by a new intermittency between the three attractors.

Third, if two conjugate quasiperiodic attractors connect with each other directly, they merge

to form a single symmetric quasiperiodic one. For the second case, the new intermittency is caused

by the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. As

the iteration number is increased, the largest finite-time Lyapunov exponent of the QC does not

converge to a constant, but fluctuates in the positive region. Published by AIP Publishing.

uncovered in the six dimensional Poincare map of a symmetric three-degree of freedom vibroimpact

system. Accompanied by symmetry restoring bifurcation, this QC is the consequence of a

novel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The six

dimensional Poincare map P is the 2-fold composition of another virtual implicit map Q, yielding

the symmetry of the system. Map Q can capture two conjugate attractors, which is at the core of

the dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzed

in detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittency

induced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenly

embedded in a chaotic one, QC is induced by a new intermittency between the three attractors.

Third, if two conjugate quasiperiodic attractors connect with each other directly, they merge

to form a single symmetric quasiperiodic one. For the second case, the new intermittency is caused

by the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. As

the iteration number is increased, the largest finite-time Lyapunov exponent of the QC does not

converge to a constant, but fluctuates in the positive region. Published by AIP Publishing.

Original language | English |
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Article number | 113121 |

Journal | Chaos |

Volume | 26 |

Issue number | 11 |

Early online date | 29 Nov 2016 |

DOIs | |

Publication status | Published - Nov 2016 |

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## Cite this

Yuan, Y., Miao, P., Xie, J., & Grebogi, C. (2016). Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system.

*Chaos*,*26*(11), [113121 ]. https://doi.org/10.1063/1.4968552