Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system

Yue Yuan, Pencheng Miao, Jianhua Xie, Celso Grebogi

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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.
Original languageEnglish
Article number113121
JournalChaos
Volume26
Issue number11
Early online date29 Nov 2016
DOIs
Publication statusPublished - Nov 2016

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Intermittency
intermittency
Chaos theory
chaos
Chaos
Bifurcation
Symmetry
symmetry
Attractor
Poincaré Map
Merging
iteration
degrees of freedom
exponents
Limit Set
Chaotic Attractor
collisions
Lyapunov Exponent
Join
Chemical analysis

Cite this

Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system. / Yuan, Yue; Miao, Pencheng; Xie, Jianhua ; Grebogi, Celso.

In: Chaos, Vol. 26, No. 11, 113121 , 11.2016.

Research output: Contribution to journalArticle

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title = "Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system",
abstract = "Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, isuncovered in the six dimensional Poincare map of a symmetric three-degree of freedom vibroimpactsystem. Accompanied by symmetry restoring bifurcation, this QC is the consequence of anovel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The sixdimensional Poincare map P is the 2-fold composition of another virtual implicit map Q, yieldingthe symmetry of the system. Map Q can capture two conjugate attractors, which is at the core ofthe dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzedin detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittencyinduced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenlyembedded 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 mergeto form a single symmetric quasiperiodic one. For the second case, the new intermittency is causedby the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. Asthe iteration number is increased, the largest finite-time Lyapunov exponent of the QC does notconverge to a constant, but fluctuates in the positive region. Published by AIP Publishing.",
author = "Yue Yuan and Pencheng Miao and Jianhua Xie and Celso Grebogi",
note = "This work was supported by National Natural Science Foundation of China (11272268, 11572263, and 11672249).",
year = "2016",
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T1 - Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system

AU - Yuan, Yue

AU - Miao, Pencheng

AU - Xie, Jianhua

AU - Grebogi, Celso

N1 - This work was supported by National Natural Science Foundation of China (11272268, 11572263, and 11672249).

PY - 2016/11

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N2 - Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, isuncovered in the six dimensional Poincare map of a symmetric three-degree of freedom vibroimpactsystem. Accompanied by symmetry restoring bifurcation, this QC is the consequence of anovel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The sixdimensional Poincare map P is the 2-fold composition of another virtual implicit map Q, yieldingthe symmetry of the system. Map Q can capture two conjugate attractors, which is at the core ofthe dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzedin detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittencyinduced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenlyembedded 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 mergeto form a single symmetric quasiperiodic one. For the second case, the new intermittency is causedby the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. Asthe iteration number is increased, the largest finite-time Lyapunov exponent of the QC does notconverge to a constant, but fluctuates in the positive region. Published by AIP Publishing.

AB - Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, isuncovered in the six dimensional Poincare map of a symmetric three-degree of freedom vibroimpactsystem. Accompanied by symmetry restoring bifurcation, this QC is the consequence of anovel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The sixdimensional Poincare map P is the 2-fold composition of another virtual implicit map Q, yieldingthe symmetry of the system. Map Q can capture two conjugate attractors, which is at the core ofthe dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzedin detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittencyinduced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenlyembedded 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 mergeto form a single symmetric quasiperiodic one. For the second case, the new intermittency is causedby the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. Asthe iteration number is increased, the largest finite-time Lyapunov exponent of the QC does notconverge to a constant, but fluctuates in the positive region. Published by AIP Publishing.

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