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中国物理学会期刊

一个三维四翼自治混沌系统的拓扑马蹄分析

CSTR: 32037.14.aps.60.010203

Topological horseshoe analysis for a three-dimensional four-wing autonomous chaotic system

CSTR: 32037.14.aps.60.010203
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  • 基于拓扑马蹄映射理论,验证了一个三维四翼自治的混沌系统的拓扑马蹄的存在.由于该混沌系统是连续系统,首先选取了一个Poincaré截面,并在该截面下定义了该混沌系统的一个一次回归Poincaré映射.通过利用计算机辅助证明方法,得出了该映射与一个2移位映射拓扑半共扼,说明该三维四翼自治系统的拓扑熵大于或等于ln2,进而证明了该系统的混沌行为.

     

    Based on topological horseshoe map theory, the paper analyses the existence of topological horseshoe in a 3-D four-wing chaotic system. As the chaotic system is continuous, the paper first choses a Poincaré section, then under which defines a first return Poincaré map. A conclusion that the Poincaré map is semi-conjugate to 2-shift map can be obtained by utilizing computer-assisted verification, showing that the topological entropy of the 3-D four-wing system is larger than or equal to ln2, which further verifies the chaotic characteristic of the system.

     

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