Coexistence of strange nonchaotic attractors and a special mixed attractor caused by a new intermittency in a periodically driven vibro-impact system

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• 作者：Yuan Yue ; Pengcheng Miao ; Jianhua Xie
• 关键词：Vibro ; impact system ; Coexistence of SNAs ; Phase ; locking ; Mixed attractor ; Intermittency ; Symmetry restoring bifurcation
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：2
• 页码：1187-1207
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

We focus on the coexistence of strange nonchaotic attractors (SNAs) and a novel mixed attractor in a periodically driven three-degree-of-freedom vibro-impact system with symmetry. SNAs are characterized by the local largest Lyapunov exponent and the phase sensitivity property. The Poincaré map P is the twofold composition of a six-dimensional implicit map Q, implying the symmetry of the vibro-impact system. Since the map Q can capture two conjugate attractors, it is used to investigate the dynamics of the system. With a suitable parameter combination, the Poincaré map P of the vibro-impact system exhibits Neimark–Sacker–pitchfork (NS-P) bifurcation. It is shown that dense phase-locking regions exist in a small parameter interval near this NS-P bifurcation point. Three types of attractors alternate in this small interval: two conjugate phase-locked periodic attractors, two conjugate SNAs and a special type of mixed attractor. As the force frequency \(\omega \) is increased gradually, many phase-locking regions disappear, and the coexistence of two conjugate SNAs takes place instead, which is accompanied by a quick decrease in the width of phase-locking. If two conjugate strange nonchaotic limit sets are suddenly embedded in a chaotic one, a special mixed attractor is caused by a new intermittency accompanied by symmetry restoring bifurcation. This symmetry restoring bifurcation is the result of the collision between two conjugate strange nonchaotic limit sets and a symmetric limit set.