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, is uncovered in the six dimensional Poincaré map of a symmetric three-degree of freedom vibro-impact 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 Poincaré 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.
authors.affiliation: Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Yue
authors.affiliation: Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China.
authors.forename: Pengcheng
authors.initials: P
authors.lastname: Miao
authors.affiliation: Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Xie
authors.affiliation: Institute for Complex Systems and Mathematical Biology King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Grebogi
authors.initials: G
authors.lastname: Celso