Multistability of a three-degree-of-freedom vibro-impact system

•Different multi-tori T2 coexist in a vibro-impact system.•The coexistence of tori T3 and tori T2 (or period-3) is verified.•High-periodic attractors and chaotic attractors coexist.•Different mechanisms leading to the multistability are investigated. Four types of scenarios occurring multistability...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2018-04, Vol.57, p.331-341
Main Authors: Zhang, Yongxiang, Luo, Guanwei
Format: Article
Language:English
Subjects:
Bifurcations
Chaos theory
Coexisting attractors
Dynamical systems
Equilibrium
Multistability
Poincaré map
Toruses
Vibro-impact
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Summary:•Different multi-tori T2 coexist in a vibro-impact system.•The coexistence of tori T3 and tori T2 (or period-3) is verified.•High-periodic attractors and chaotic attractors coexist.•Different mechanisms leading to the multistability are investigated. Four types of scenarios occurring multistability are identified in a vibro-impact system. Besides the coexistence of high-periodic attractors and chaotic attractors, this system has some coexisting multi-frequency quasiperiodical attractors. We observe the coexistence of different two-dimensional tori T2, which the mechanism of torus formation involves phase-locked dynamics on three-dimensional tori. We also find that the tori T3 and the tori T2 (or period-3) coexist for a certain set of parameters. The mechanism leading to the multistability is investigated through interplay among the codimension two bifurcations, strong resonance bifurcations and global bifurcations.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.10.007