Constructing chaotic systems with conditional symmetry

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• 作者：Chunbiao Li ; Julien Clinton Sprott ; Hongyan Xing
• 关键词：Conditional symmetry ; Offset boosting ; Multistability
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：2
• 页码：1351-1358
• 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

Asymmetric dynamical systems sometimes admit a symmetric pair of coexisting attractors for reasons that are not readily apparent. This phenomenon is called conditional symmetry and deserves further explanation and exploration. In this paper, a general method for constructing such systems is proposed in which the asymmetric system restores its original equation when some of the variables are subjected to a symmetric coordinate transformation combined with a special offset boosting. Two regimes of this conditional symmetry are illustrated in chaotic flows where a symmetric pair of attractors resides in asymmetric basins of attraction.